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Yakov Sinai
Yakov Grigorevich Sinai (Russian: Я́ков Григо́рьевич Сина́й; born September 21, 1935) is a mathematician known for his work on dynamical systems
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Russian SFSR
"The Internationale" (1918–1944)"National Anthem of the Soviet Union" (1944–1990)"The Patriotic Song" (1990–1991)Extent of the Russian SFSR
Russian SFSR
(red) within the Soviet Union (red and white) following World War II
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Ergodic Hypothesis
In physics and thermodynamics, the ergodic hypothesis[1] says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are equiprobable over a long period of time. Liouville's Theorem states that, for Hamiltonian systems, the local density of microstates following a particle path through phase space is constant as viewed by an observer moving with the ensemble (i.e., the convective time derivative is zero). Thus, if the microstates are uniformly distributed in phase space initially, they will remain so at all times. But Liouville's theorem does not imply that the ergodic hypothesis holds for all Hamiltonian systems. The ergodic hypothesis is often assumed in the statistical analysis of computational physics
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Soviet Union
The Soviet Union
Soviet Union
(Russian: Сове́тский Сою́з, tr. Sovétsky Soyúz, IPA: [sɐˈvʲɛt͡skʲɪj sɐˈjus] ( listen)), officially the Union of Soviet Socialist Republics (Russian: Сою́з Сове́тских Социалисти́ческих Респу́блик, tr. Soyúz Sovétskikh Sotsialistícheskikh Respúblik, IPA: [sɐˈjus sɐˈvʲɛtskʲɪx sətsɨəlʲɪsˈtʲitɕɪskʲɪx rʲɪˈspublʲɪk] ( listen)), abbreviated as the USSR (Russian: СССР, tr. SSSR), was a socialist state in Eurasia
Eurasia
that existed from 1922 to 1991. Nominally a union of multiple national Soviet republics,[a] its government and economy were highly centralized. The country was a one-party state, governed by the Communist Party with Moscow
Moscow
as its capital in its largest republic, the Russian Soviet Federative Socialist Republic
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Konstantin Khanin
Konstantin "Kostya" Mikhailovich Khanin (Russian: Константин Михайлович Ханин) is a Russian mathematician and physicist. Khanin received his PhD from the Landau Institute of Theoretical Physics in Moscow and continued working there as a research associate until 1994.[1] Afterwards, he taught at Princeton University, at the Isaac Newton Institute
Isaac Newton Institute
in Cambridge, and at Heriot-Watt University
Heriot-Watt University
before joining the faculty at the University of Toronto. Khanin was an invited speaker at the European Congress of Mathematics in Barcelona in 2000
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Leonid Polterovich
Leonid Polterovich
Leonid Polterovich
(Hebrew: ליאוניד פולטרוביץ‎; Russian: Леонид В. Полтерович; born 30 August 1963) is a Russian-Israeli mathematician at Tel Aviv University. His research field includes symplectic geometry and dynamical systems. A native of Moscow, Polterovich earned his undergraduate degree at Moscow
Moscow
State University in 1984. He moved to Israel
Israel
after the collapse of communism, earning his doctorate from Tel Aviv University
Tel Aviv University
in 1990. In 1996, he was awarded the EMS Prize,[1] and in 1998 the Erdős Prize. He was a member of the faculty of the University of Chicago. References[edit]^ "Archived copy". Archived from the original on 2012-03-28
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Russian Language
Russian (Russian: ру́сский язы́к, tr. rússkiy yazýk) is an East Slavic language
East Slavic language
and an official language in Russia, Belarus, Kazakhstan, Kyrgyzstan
Kyrgyzstan
and many minor or unrecognised territories throughout Eurasia
Eurasia
(particularly in Eastern Europe, the Baltics, the Caucasus, and Central Asia). It is an unofficial but widely spoken language in Latvia, Moldova, Ukraine
Ukraine
and to a lesser extent, the other post-Soviet states.[31][32] Russian belongs to the family of Indo-European languages
Indo-European languages
and is one of the four living members of the East Slavic languages
Slavic languages
(which in turn is part of the larger Balto-Slavic branch)
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics
Mathematics
is concerned with numbers, data, quantity, structure, space, models, and change.Contents1 History 2 Required education 3 Activities3.1 Applied mathematics 3.2 Abstract mathematics 3.3 Mathematics
Mathematics
teaching 3.4 Consulting4 Occupations 5 Quotations about mathematicians 6 Prizes in mathematics 7 Mathematical autobiographies 8 See also 9 Notes 10 References 11 Further reading 12 External linksHistory This section is on the history of mathematicians
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Dynamical Billiards
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed. Billiard dynamical systems are Hamiltonian idealizations of the game of billiards, but where the region contained by the boundary can have shapes other than rectangular and even be multidimensional. Dynamical billiards
Dynamical billiards
may also be studied on non-Euclidean geometries; indeed, the very first studies of billiards established their ergodic motion on surfaces of constant negative curvature. The study of billiards which are kept out of a region, rather than being kept in a region, is known as outer billiard theory. The motion of the particle in the billiard is a straight line, with constant energy, between reflections with the boundary (a geodesic if the Riemannian metric of the billiard table is not flat)
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Ergodic
In probability theory, an ergodic dynamical system is one that, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states in its phase space. In physics the term implies that a system satisfies the ergodic hypothesis of thermodynamics. A random process is ergodic if its time average is the same as its average over the probability space, known in the field of thermodynamics as its ensemble average. The state of an ergodic process after a long time is nearly independent of its initial state.[1] The term "ergodic" was derived from the Greek words έργον (ergon: "work") and οδός (odos: "path," "way")
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Alexander Esenin-Volpin
Alexander Sergeyevich Esenin-Volpin (also written Ésénine-Volpine and Yessenin-Volpin in his French and English publications; Russian: Алекса́ндр Серге́евич Есе́нин-Во́льпин; May 12, 1924 – March 16, 2016) was a prominent Russian-American poet and mathematician. A notable dissident, political prisoner and a leader of the Soviet human rights movement, he spent a total of fourteen years incarcerated and repressed by the Soviet authorities in prisons, psikhushkas and exile.Contents1 Life1.1 The Glasnost demonstration 1.2 Emigration2 Mathematical work 3 Mathematical publications 4 References 5 Further reading 6 External links 7 Audio-visual materialLife[edit] Alexander Volpin was born on May 12, 1924 in the Soviet Union. His mother, Nadezhda Volpin, was a poet and translator from French and English. His father was Sergei Yesenin,[1]:221 a celebrated Russian poet, who never knew his son
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Leonid Bunimovich
Leonid Bunimovich is a Soviet and American mathematician, who specializes in dynamical systems. He is known for discovery of a fundamental mechanism of chaos (hyperbolicity) in Dynamical systems, which is called mechanism of defocusing. The most famous class of chaotic dynamical systems of this type Dynamical billiards are focusing chaotic billiards (e.g., the "Bunimovich stadium","Bunimovich flowers", etc.). More recently he introduced so called Bunimovich mushrooms, which are visual examples of billiards with mixed regular and chaotic dynamics. In many labs over the world were built experimental devices in the form of various Bunimovich billiards. He received bachelor's degree in 1967 and PhD in 1973 from the University of Moscow. His thesis adviser was Yakov G. Sinai. In 1986 he was awarded Doctor of Sciences degree in "Theoretical and Mathematical Physics". Bunimovich is a Regents' Professor of Mathematics at the Georgia Institute of Technology
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California Institute Of Technology
The California
California
Institute of Technology (abbreviated Caltech)[8] is a private doctorate-granting university located in Pasadena, California, United States and is considered one of the leading universities in the world in science and technology. Although founded as a preparatory and vocational school by Amos G. Throop in 1891, the college attracted influential scientists such as George Ellery Hale, Arthur Amos Noyes
Arthur Amos Noyes
and Robert Andrews Millikan
Robert Andrews Millikan
in the early 20th century. The vocational and preparatory schools were disbanded and spun off in 1910 and the college assumed its present name in 1921
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Moscow Mathematical Journal
The Moscow Mathematical Journal is a mathematics journal published quarterly by the Independent University of Moscow and the HSE Faculty of Mathematics and distributed by the American Mathematical Society. The journal published its first issue in 2001. Its editors-in-chief are Yulij Ilyashenko (Independent University of Moscow and Cornell University), Michael Tsfasman (Independent University of Moscow and Aix-Marseille University), and Sabir Gusein-Zade (Moscow State University and the Independent University of Moscow). External links[edit]Official websiteThis article about a mathematics journal is a stub. You can help by expanding it.v t eSee tips for writing articles about academic journals
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Norwegian Academy Of Science And Letters
The Norwegian Academy of Science and Letters
Norwegian Academy of Science and Letters
(Norwegian: Det Norske Videnskaps-Akademi, DNVA) is a learned society based in Oslo, Norway.Contents1 History 2 Organisation 3 References 4 External linksHistory[edit] The Royal Frederick University
Royal Frederick University
in Christiania was established in 1811. The idea of a learned society in Christiania surfaced for the first time in 1841.[1] The city of Trondhjem had no university, but had a learned society, the Royal Norwegian Society of Sciences and Letters, established in 1760.[2] The purpose of a learned society in Christiania was to support scientific studies and aid publication of academic papers. The idea of the Humboldt-inspired university, where independent research stood strong, had taken over for the instrumental view of a university as a means to produce civil servants
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Ergodic Theory
Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the phase space eventually revisit the set. More precise information is provided by various ergodic theorems which assert that, under certain conditions, the time average of a function along the trajectories exists almost everywhere and is related to the space average. Two of the most important theorems are those of Birkhoff (1931) and von Neumann which assert the existence of a time average along each trajectory
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