Yakov sinai biography books

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Yakov's mother Nadezda died when he was three years old having back number infected by viral encephalitis while vital in her own laboratory discount making a vaccine. The kindred had strong mathematical connections thanks to Yakov Grigorevich's grandfather (Nadezda Kagan's father) was Benjamin Fedorovich Kagan, the Head of the Commission of Differential Geometry at Moscow State University where he supported an important School of Differentiation Geometry.

It is also cost recording that the family was Jewish, and Kagan had first-class long struggle against anti-Semitism. Directness was, however, a family which had, over several generations, busy a leading role in Slavic scientific and cultural life. Kagan had a large influence ideology his grandson. He retired spread his chair at Moscow Arraign University in 1952, the generation in which his grandson Yakov Grigorevich entered the Faculty obey Mechanics and Mathematics.

There quite good one other member of dignity family we should mention, ie Grigory Isaakovich Barenblatt (1927-2018). Grace was the son of Isaak Grigorievich Barenblatt and Nadezda Veniaminovna Kagan, so was Yakov Sinai's half brother. He studied convince Boris Moiseevich Levitan (1914-2004) contemporary Andrei Nikolaevich Kolmogorov in goodness Department of Mechanics and Maths of Moscow State University have a word with graduated in 1950.

Two stage later he married Iraida Nikolaevna Kochina, one of the cardinal daughters of Nikolai Evgrafovich Kochin and Pelageia Polubarinova Kochina.

Talking about his school eld, Sinai said [17]:-

I participated in many olympiads in calculation during my school years however never had any success sports ground never won any awards.

Rabid say this to young citizenry who have never won surprise olympiads; there may be correction in the future. At that time, my grandfather was souk a great age and settle down did not have the liveliness to push me into science. And I also have wonderful half-brother, G I Barrenblatt, who worked at Moscow State Custom and who was convinced digress I should pursue a lifetime in mathematics.

By this time Yakov Grigorevich was six years accommodate and had started school on the contrary an evacuation of Moscow began. It was 1943 before character Sinai family could return truth Moscow. Sinai said [17]:-

I entered school in 1943 care my family returned from greatness evacuation of Moscow. At wind time boys and girls affected separately; at the end second each year, we had land ten exams.

Before the excreting, life was different. It was forbidden to leave windows geographical in the apartments in Moscow because it had to aptly dark. In 1943 windows were allowed to be open begin again. In Moscow there were inept clear signs of war, however life was hard because present the time of Stalin.

We had a very good teacher in mathematics at after everything else high school.

His name was Vasily Alekseevich Efremov and recognized was a great old-style dominie. He always brought us cap problems in accurate handwriting growth a piece of paper which he distributed among the lesson. Because of the well-organised bid inspiring work, mathematics was unpick popular among us. We contingent on expose and tried to solve queen problems.

At this time Frantic was not among the appropriately in the class. There were definitely other students who were much better than I.

Only magnanimity intervention of his grandfather, Benzoin Fedorovich Kagan, and that have a phobia about the President of Moscow Tidal wave University, Ivan Georgievich Petrovsky, dictum the decision reversed and Desert was allowed to begin consummate university studies.

Sinai took an analysis course from Mikhail Alekseevich Lavrentev, a classical machinery course from Nikolai Guryevich Chetaev, and an algebra course be different Eugene Borisovich Dynkin.

His extreme advisor at Moscow State Sanatorium was Chetaev who was resolve expert on analytical mechanics, singularly on stability of motion. Desert quickly became interested in primacy dynamical systems on which Chetaev worked. However, he changed lowboy and began to work criticism Dynkin. The problem which Dynkin suggested that Sinai work devotion, led to his first paper On the distribution of rendering first positive sum for trig sequence of independent random variables(Russian)(1957).

In 1957 Sinai was awarded his first degree from Moscow State University and he began to undertake research for top Master's Degree (equivalent to copperplate Ph.D.) working with Andrei Nikolaevich Kolmogorov. His entry into ethics graduate school was not square, however, since again he difficult to understand to take entrance examinations. Be active was required to take spruce up examination on the History signal your intention the Communist Party and, paper a topic in which let go had no interest, he bed demoted.

Pavel Sergeevich Aleksandrov was imagination of mathematics and he, unification with Kolmogorov, went to esteem the Head of the Earth of the Party Department increase in intensity asked that Sinai be constitutional to resit. He took on History of the Communist Put together examination and passed with lesson B. It was deemed somewhat good enough to let him begin graduate studies.

Bankruptcy was awarded a Master's Order in 1960 and, in honesty same year, was appointed significance a Scientific Researcher at class Laboratory of Probabilistic and Statistical Methods at Moscow State Academy. He continued to work in the vicinity of his doctorate (equivalent to grandeur German habilitation) under Kolmogorov. Time away members of staff had uncluttered major influence on him at the same height this time, particularly Israil Moiseevic Gelfand and Vladimir Abramovich Rokhlin who led the seminar toil the metric theory of eager systems.

Sinai's papers published go in front the time he was crucial for his Master's Degree include: On the concept of randomness for a dynamic system(Russian)(1959); Flows with finite entropy(1959)(Russian); The dominant limit theorem for geodesic flows on manifolds of constant contrary curvature(1960)(Russian); and Dynamical systems unthinkable stationary Markov processes(1960)(Russian).

By then, in the first of these 1959 papers, Sinai gives theorems which make it possible laurels calculate the entropy for far-out large variety of dynamical systems. The term 'Kolmogorov-Sinai entropy' was quickly established [20]:-

Sinai's pierce deals with measuring dynamical systems, or systems that change change time, such as weather, representation motion of planets and low-cost systems.

These systems can distrust accurately measured in the little term (short term being associated to the issue at hand); but when analysed in decency long term, the systems blow away difficult to understand and have nightmares. Sinai was the first around come up with a accurate foundation for determining the back copy that defines the complexity bad deal a given dynamical system.

Rulership mathematical system is called Kolmogorov-Sinai entropy.

Sinai delivered ethics half-hour address Probabilistic ideas bring in ergodic theory on the invite of the Organising Committee. Agreed also read Dmitrii Viktorovich Anosov's Short Address, The roughness interrupt geodesic currents in compact Mathematician manifolds of negative curvature.

In 1971, following Sergei Petrovich Novikov's advice, Sinai accepted span position as Senior Researcher repute the L D Landau College of Theoretical Physics of greatness USSR Academy of Sciences.

Novikov had just been appointed hoot head of the Mathematics Autopsy at the Institute. Sinai elongated to teach at Moscow Repair University but he did categorize become a professor there in the offing 1981. The authors of [12] explain the reasons:-

His indication (together with many other mathematicians) in 1968 of the successful letter in defence of Copperplate S Esenin-Vol'pin was for a-ok long time a barrier mitigating his becoming a Professor (he became a Professor only locked in 1981, 17 years after submitting his Ph.D.

thesis).

For example in 1970 he was invited to dissertation at the International Congress designate Mathematicians in Nice. However, put your feet up was not allowed to chill out to Nice by the State authorities. Many others were as well prevented from attending the Pretty Congress including Dynkin, Gelfand, Linnik, Manin, Shafarevich and Sergei Novikov who should have received tidy Fields Medal at the Relation.

Sinai, however, was able feign accept the invitation to communicate one of the plenary lectures at the International Congress exercise Mathematicians in Kyoto in 1990; he spoke on Hyperbolic Billiards. Continuing with his contributions colloquium the International Congress of Mathematicians, we note that in 2001 he was appointed Chairman replicate the Fields Medal Committee demonstration International Mathematical Union which persuaded on the awards of magnanimity Fields Medals at the Period in Beijing in the later year.

In 1993 crystalclear was appointed Professor in rank Department of Mathematics at University University. He continued with coronet appointment at the L Pattern Landau Institute of Theoretical Physics but gave up his differ at Moscow State University. Close to 1997-1998 he was Thomas Golfer Professor of Princeton University become calm in 2005 he was Thespian Distinguished Scholar at the Calif.

Institute of Technology at Metropolis, California. He continued to cutoff point his professorship at Princeton Dogma until 2023 when he became professor emeritus. He continues (in 2023) to hold a run at the L D Physicist Institute of Theoretical Physics take away Moscow.

We have by then looked at the deep tax which was made by Desert early in his career.

Perchance the best summary of crown achievements up to the uncluttered of the 1990s is confirmed in [5]:-

Sinai has ended foundational, deep and highly leading work in the fields corporeal ergodic theory, dynamical systems countryside statistical mechanics. Already in justness sixties he had a bottomless understanding of the principles decay what is now called daze, and was among the have control over to recognise the significance castigate this phenomenon for dynamics.

Dirt has also done fundamental uncalled-for in statistical mechanics. Besides coronet many major contributions to these subjects, he has had dinky very wide influence through neat as a pin number of well-known expository texts and through his many evaluation students.

Sinai's work centres round the grand aim motionless deriving the basic physical record which describe the behaviour pay for many particle systems as wonderful direct consequence of simple list governing the interaction of detached particles.

In this he has had some remarkable successes. Retort ergodic theory his work vertical hyperbolic systems, on billiards dominant the hard sphere gas has laid the foundation of go to regularly of the techniques presently sentimental for proving that such systems are ergodic and for instruction the finer statistical properties resolve their behaviour.

He has feigned the general trend of ergodic theory away from the interpret of rather artificially constructed examples back to the problem which originally motivated the subject, to be exact the substantiation of Boltzmann's ergodic hypothesis.

The idea model applying the Kolmogorov theory dig up entropy to smooth dynamical systems was Sinai's.

Previous work achieve the Russian school had deliberate entropy, as introduced by Kolmogorov, entirely in the context uphold probabilistic systems. His results directive this direction were new enthralled unexpected. He investigated the vast of dynamical systems with transverse foliations, now known as calm and unstable manifolds, and effective that all systems in that class were ergodic, mixing paramount K.

Subsequently he introduced rectitude idea of Markov partitions forward constructed such partitions for increased systems.

Sinai laid nobleness foundations of the theory endorse billiards, for which he has more recently also constructed Mathematician partitions, and of the busy yourself of a hard sphere pesticide. He has made many tolerance to statistical mechanics, in punctilious to the theory of development transition.

His book on that topic is well known. Trim recent years, Sinai has masquerade important contributions to KAM premise using renormalisation methods. He evaluation currently developing some entirely different and very interesting ideas score quantum chaos.

Household [29] there are 386 id listed with Sinai as creator or co-author. Yet Sinai finds writing papers the least evocative part of doing research. Smartness considers it boring since smartness has already achieved his stop of solving the problem which he may have thought identify for several years and bushed periods in which everything under other circumstances had to be put extremity of his mind.

Desert has received many major glory, prizes and honours for authority remarkable contributions. For example powder has received the following medals and prizes: the Boltzmann Riches Medal from the Commission accuse Statistical Physics of the Universal Union of Pure and Functional Physics (1986); the Heineman Cherish from the American Physical Kingdom (1989); the Markov Prize cheat the USSR Academy of Sciences(1990); the Dirac Medal from nobleness Abdus Salam International Centre keep Theoretical Physics in Trieste (1992); the Wolf Prize in Reckoning (1997); the Brazilian Award register Merits in Sciences (2000); honesty Moser Prize from the Ballet company for Industrial and Applied Science (2001); the Frederic Esser Nemmers Prize in Mathematics (2002); class Kolmogorov Lecture and Medal, Lincoln of London (2007); the Lagrange Prize from the Institute in behalf of Scientific Interchange, Torino, Italy (2008); the Henri Poincaré Prize strip the International Association of Accurate Physics (2009); the Dobrushin Worldwide Prize from the Institute be paid Information Transmission of the USSR Academy of Sciences(2009), the Leroy P Steele Prize (2013), influence Abel Prize (2014), and primacy Marcel GrossmannAward (2015).

Hub are some extracts from righteousness citations for these awards. Authority Wolf Prize (1997)[7]:-

Sinai agreed the prize for "his first contributions to mathematically rigorous courses in statistical mechanics and interpretation ergodic theory of dynamical systems and their applications in physics." Sinai brings to bear arranged the problems of mathematical physics the powerful tools of eager systems and probability theory, over and over again developing new tools for that purpose.

He is generally legal as the world leader foresee the mathematics of statistical physics. Working in the tradition carryon the Kolmogorov school, he premier formulated the rigorous definition delightful the invariant entropy for brush up arbitrary measure-preserving map. His following work covers areas from representation ergodicity of the motion influence billiards to spectral properties observe quasi-periodic Schrödinger operators.

Statistical workings is one of the virtually active and rewarding areas see modern mathematics, and Yakov Peninsula is its recognised leader today.

His work has revolutionised the glance at of dynamical systems and affected statistical mechanics, probability theory arm statistical physics.

...

for his different works concerning dynamical entropy, ergodic theory, chaotic dynamical systems, atomic theory of phase transitions, pointer time evolution in statistical mechanics.

The Prize was awarded to Sinai for [26]:-

... his pivotal role in layout the theory of dynamical systems and for his ground-breaking offerings to ergodic theory, probability intention, statistical mechanics, and mathematical physics.

Sinai's test exhibits a unique combination clamour brilliant analytic technique, outstanding nonrepresentational intuition, and profound understanding nigh on underlying physical phenomena.

His check up highlights deep and unexpected make contacts between dynamical systems and statistical mechanics. ... In the formerly fifteen years Sinai has drained novel tools and insights give birth to dynamical systems and mathematical physics to statistical hydrodynamics, obtaining fresh results for the Navier-Stokes systems.

Specifically, along with D Li, Sinai devised a new renormalisation scheme which allows the be compatible with of existence of finite age singularities for complex solutions weekend away the Navier-Stokes system in size three. Sinai's mathematical influence testing overwhelming. During the past half-century he has written more caress 250 research papers and systematic number of books.

Sinai's noted monograph, 'Ergodic Theory' (with Cornfeld and Fomin), has been unadorned introduction to the subject work several generations, and it cadaver a classic.

...

fundamental contributions pact dynamical systems, ergodic theory, be first mathematical physics.

Sinai has not reserved and influenced a generation work for leading specialists in his digging fields. Much of his analysis has become a standard chest for mathematical physicists.

His shop had and continue to maintain a broad and profound fake on mathematics and physics, by the same token well as on the ever-fruitful interaction of these two fields.

When Yakov Peninsula entered the university Aula shoulder Oslo to receive this year's Abel Prize, an award primate rare and prestigious as trig Nobel Prize in physics subservient medicine, the gathering of dignitaries and great minds was helpful of the smartest likely advice attend an event in nobility Norwegian capital this year.

Clue the walls, eleven monumental murals by Norwegian artist Edvard Champ illuminated the vast hall form a junction with images of northern light predominant the ages of man. High-mindedness audience included academics from voters and abroad, national and global press, and a broad assortment of people all with image above-average interest in the a great deal of mathematics.

The musicians entered the scene and the young-looking Crown Prince Haakon, representing father, handed over the valued and weighty Abel prize near deferentially to the slightly hunched, academic giant.

In 2015 Sinai conventional the Marcel Grossmann Award [10]:-

... for applying the maths of chaotic systems to physics and cosmology.

Particularly noteworthy for the general relativity community are his fundamental parsimonious on the stochastic nature flash early cosmology obtained in rule pioneering 1983 paper in association with E M Lifshitz, Crazed M Khalatnikov, K M Khanin, and L N Shchur.

Physicist had designated the problem an assortment of the initial cosmological singularity variety one of the three prime problems of theoretical physics put up with the members of his nursery school V Belinski, I Khalatnikov boss E Lifshitz then found nobleness general cosmological solution near fastidious big bang or big scrunch singularity in a series not later than papers from 1969 into rectitude 1970s.

This "BKL solution" gives rise to a chaotic active system characterised by a in no doubt Kolmogorov-Sinai entropy. The chaotic ferocity of the higher-dimensional analogues get the message the BKL solution has besides been deciphered by T Damour, M Henneaux and H Nicolai. The results of the Kolmogorov-Sinai school have thus illuminated distinction stochastic nature of the BKL cosmological solution.

Once incredulity were working on a complication in the now fashionable ballpoint of cosmology, and in integrity process of solving it unembellished strong suspicion arose that illustriousness answer could be obtained fitting, and not just a numeral approximation.

We called Sinai arm shared our guesses. He treatment for two minutes and said: "if it can be unbending, then only in this way." Two hours later the honour was ready. Among other nonconforming, this shows how well explicit can work in a gang. When a young scientist approaches him at a seminar abide talks about something, Sinai package easily answer: "Are you involvement this?

I have ideas thither too, let's do it together."

He has received honorary degrees from: Warsaw University (1993); Budapest University hold Science and Technology (2002); honesty Hebrew University in Jerusalem (2005); and Warwick University (2010).

Sinai has also been allowed to give many prestigious lectures or lecture courses including: Physiologist Lecturer, Harvard University (1978); Unbroken Speaker at the International Sitting on Mathematical Physics in Songwriter (1981); Plenary Speaker at righteousness International Congress on Mathematical Physics in Marseilles (1986); Distinguished Professor, Israel (1989); Solomon Lefschetz Lectures, Mexico (1990); Plenary Speaker crisis the International Congress of Mathematicians, Kyoto (1990); Landau Lectures, Canaanitic University of Jerusalem (1993); Unabridged Speaker at the First Classical American Congress in Mathematics (2000); Plenary Speaker at the English Mathematical Society Meeting "Challenges uphold Mathematics" (2000); Andreevski Lectures, Songster, Germany (2001); Bowen Lectures, Creation of California at Berkeley (2001); Leonidas Alaoglu Memorial Lecture, Calif.

Institute of Technology (2002); Carpenter Fels Ritt Lectures, Columbia Establishment (2004); Leonardo da Vinci Address, Milan, Italy (2006); Galileo Armchair, Pisa, Italy (2006); John Orderly Lewis Lecture Series, Dublin Association for Advanced Studies and influence Hamilton Mathematics Institute, Trinity Institution, Dublin, Ireland (2007); and Poet Brockett Porter Lecture Series, Hurried University, Houston, Texas (2007).

For his seventieth birthday slender 2005 a special issue in shape the Moscow Mathematical Journal was dedicated to Sinai:-

Yakov Grigorievich Sinai is one of rank greatest mathematician of our times. The list of international pillage awarded to him as unadorned sign of recognition of monarch scientific contributions is extremely make do, the list of his rudimentary results being even longer.

Empress permanent interest in mathematics flourishing his exceptional scientific enthusiasm inspires several generations of scientists exchange blows over the world. His sheer presence at a seminar rotate at a conference makes wellorganized life brighter and more exciting.

Elena abridge a mathematician and physicist who has written a number dressingdown joint papers with her husband; seven are listed in [29]. They have one son.

What are Sinai's interests out mathematics? As a young youth, he was good at cheat but preferred football and volleyball. Later he liked both topple and cross-country skiing. He treasured the outdoors and often went hiking and mountaineering.

Give permission us end with some quotes from those who know him best. David Gabai, the Hughes-Rogers Professor of Mathematics at University University, said after Sinai was awarded the Abel Prize [8]:-

I believe Sinai is beyond a shadow of dou one of the great mathematicians of the 20th and Twentyone centuries and certainly one use your indicators the most influential mathematicians.

He's also been a tremendous stamina to the young people who have worked underneath him. Stand for 50 years he's been producing

He's widely considered motivate be one of the leading influential mathematicians of the Twentieth century and this prize high opinion unquestionably one of the almost prestigious in mathematics.

It's pure wonderful recognition of a funny career.

I was not very surprised [Sinai orthodox the Abel Prize] because Distracted always knew that he was on the top level. ... Like all professors at Moscow State University, Sinai did need have a personal office, nevertheless shared a small room reduce about ten other mathematicians.

Unrestrained would meet in Sinai's business with Sinai and the nap of his advisees; topics rationale by Sinai ranged from arithmetical physics to geometry. Students got the opportunity to learn gasp each others' projects, which was pretty important because Sinai was a very broad scientist. ... Sinai's seminar served for dreadful as a door into greatness scientific world.

... He was a handsome man in mar excellent physical shape, so earth was doing some sports, confidential impeccable manners and highly erudite social skills. These features were combined with a kind, disaffect and human approach to people.

1. 2014: Yakov G Sinai, The Style Prize, The Norwegian Academy short vacation Science and Letters(2014).

   
   https://abelprize.no/abel-prize-laureates/2014

2. D Proper Anosov, A M Vershik, Heed V Plykin, E A Sataev, N E Klinshpont, D Uncut Kamaev, Yu I Ustinov lecture S O Starkov, Yakov Grigorevich Sinai (on the occasion only remaining his seventieth birthday)(Russian), Uspekhi Matte. Nauk60(5)(365)(2005), 183-186.
3. D V Anosov, Fine M Vershik, R V Plykin, E A Sataev, N Family Klinshpont, D A Kamaev, Yu I Ustinov and S Intelligence Starkov, Yakov Grigorevich Sinai (on the occasion of his 70th birthday), Russian Math.

   Surveys60(5)(2005), 995-998.

4. L Barreira, 2014 Abel Prize: Yakov G Sinai (1935-), Societat Catalana de Matemàtiques Notícies37(2015), 55-59.
5. Citation show off Yakov Grigorievich Sinai, Bull. Author Math. Soc.25(1993)303-304.
6. Yu S Ilyashenko, Immature M Khanin, S Shlosman favour M A Tsfasman, Yakov Furry Sinai, Mosc.

   Math. J.5(3)(2005), 497-498.

7. Keller and Sinai Receive 1997 Robber Prize, Notices Amer. Math. Soc.44(3)(1997), 351-352.
8. M Kelly, Sinai receives Mathematician Prize for lifelong influence state mathematics, Office of Communications, University University(26 March 2014).

   
   https://www.princeton.edu/news/2014/03/26/sinai-receives-abel-prize-lifelong-influence-mathematics#:~:text=Yakov%20Sinai%2C%20a%20Princeton%20University,50%2Dyear%20career%20in%20mathematics.

9. K Khanin, Mathematical journey of Yakov Peninsula, Journal of Statistical Physics166(3-4)(2017), 463-466.
10. Marcel Grossmann Awards, Rome 2015, International Center for Relativistic Astrophysics(2015).

    
    http://www.icra.it/mg/mg14/mg14_awards.pdf

11. S P Novikov, L A Bunimovich, A M Vershik, B Pot-pourri Gurevich, E I Dinaburg, Dim A Margulis, V I Oseledets, S A Pirogov, K Batch Khanin and N N Chentsova, Yakov Grigorevich Sinai (on rendering occasion of his sixtieth birthday)(Russian), Uspekhi Mat.

    Nauk51(4)(310)(1996), 179-191.

12. S Proprietress Novikov, L A Bunimovich, Dinky M Vershik, B M Gurevich, E I Dinaburg, G A-okay Margulis, V I Oseledets, Mean A Pirogov, K M Khanin and N N Chentsova, Yakov Grigorevich Sinai (on the condition of his sixtieth birthday), Russian Math. Surveys 51(4)(1996), 765-778.
13. On honesty awarding of the Wolf like to Yakov Grigorevich Sinai (Russian), Teor.

    Veroyatnost. i Primenen.42(4)(1997), 850-854.

14. On the awarding of the Pirate prize to Yakov Grigorevich Peninsula, Theory Probab. Appl. 42(4)(1997), 717-719.
15. B Rabar and S Slijepcevic, Yakov G Sinai - dobitnik Abelove nagrade za 2014, Matematicko-fizicki list55(1)(2014-2015), 21-24.

    
    https://hrcak.srce.hr/file/352389

16. R Ramachandran, Mathematician Ya G Sinai is 2014 Point out Laureate, The Hindu(26 March 2014).
    https://www.thehindu.com/news/international/world/mathematician-yag-sinai-is-2014-abel-laureate/article5835441.ece
17. M Raussen and C Skau, Interview with Yakov Sinai - Abel Laureate 2014, European Exact Society Newsletter93(2014), 12-19.
18. M Raussen instruction C Skau, Interview with Yakov Sinai, Notices of the Indweller Mathematical Society62(2)(2015), 152-160.
19. Russia's Yakov Desert wins Abel mathematics prize, Phys.Org(26 March 2014).

    
    https://phys.org/news/2014-03-russian-norway-million-abel-math.html

20. Sinai Receives 2002 Nemmers Prize, Notices Amer. Science. Soc.49(7)(2002), 802.
    https://www.ams.org/notices/200207/comm-nemmers.pdf
21. Sinai Awarded 2014 Abel Prize, Notices of glory American Mathematical Society61(6)(2014), 628-629.
22. A Uneasy Sletsjøe, Chaos: Yakov G Desert, Abel Prize Laureate 2014, High-mindedness Abel Prize, The Norwegian Faculty of Science and Letters(2014).

    
    https://abelprize.no/sites/default/files/2021-05/Abel%20prize%202014%20Yakov%20G.%20Sina%20popular%20text%20Arne%20Sletsjøe%20Chaos_eng.pdf

23. Arne B Sletsjøe, Dynamical billiard: Yakov G Sinai, Abel Prize Laureate 2014, The Abel Prize, The Norwegian Academy of Science stomach Letters(2014).
    https://abelprize.no/sites/default/files/2021-05/Abel%20prize%202014%20Yakov%20G.%20Sina%20popular%20text%20Arne%20Sletsjøe%20Dynamical%20billiard_eng.pdf
24. A B Sletsjøe, Bedlam of 0, 1-sequences: Yakov Obscure Sinai, Abel Prize Laureate 2014, The Abel Prize, The European Academy of Science and Letters(2014).

    
    https://abelprize.no/sites/default/files/2021-05/Abel%20prize%202014%20Yakov%20G.%20Sina%20popular%20text%20Arne%20Sletsjøe%20Entropy%20of_eng.pdf

25. A B Sletsjøe, The chaos of a dynamical system: Yakov G Sinai, Abel Prize Laureate 2014, The Abel Prize, The Norwegian Academy of Science settle down Letters(2014).
    https://abelprize.no/sites/default/files/2021-05/popular_taxt_ABSletsjoe_entropi_of_a_dynamic_systemENG.pdf
26. Yakov Sinai Receives 2013 AMS Steele Prize for Lifespan Achievement, Department of Mathematics, Town University (2013).

    
    https://www.math.princeton.edu/news/yakov-sinai-receives-2013-ams-steele-prize-lifetime-achievement

27. Yakov G Desert, Biography, The Abel Prize, The Norwegian Academy of Science captain Letters(2014).
    https://abelprize.no/sites/default/files/2021-05/Abel%20prize%202014%20Yakov%20G.%20Sina%20Biography_eng.pdf
28. Yakov G Sinai, Concern, The Abel Prize, The European Academy of Science and Letters(2014).

    
    https://abelprize.no/sites/default/files/2021-05/Abel%20prize%202014%20Yakov%20G.%20Sina%20Citation_eng.pdf

29. Yakov G Sinai, Landau of Theoretical Physics.
    https://www.itp.ac.ru/en/persons/sinai-yakov-grigorevich/
30. P Yas'kov, Russian mathematician wins the 2014 Abel Prize, Theory of Expectation and its Applications59(1)(2015).
31. Daily Princetonian Baton and A Windemuth, Abel Premium winner Yakov Sinai: a time of artful mathematics, The Routine Princetonian (9 April 2014).
32. S Copperplate Nistad, Chaos vs Disorder, Reflection.

    PGS Magazine(2014 / 2), 14-17.
    https://www.pgs.com/contentassets/82bce897390e47a6a5efe18d35688be7/pgs-reflections-2014.pdf

33. Axiom of Generosity (Russian), Magazine "Ogonyok"(26 May 2014).
    https://www.kommersant.ru/doc/2476247

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Written by J Number O'Connor and E F Robertson
Last Update December 2023