page_title: Leonid Bunimovich
hierarchical_section_title: Leonid Bunimovich
caption_attribution_description: English: Leonid Bunimovic, Russian mathematician.
context_page_description: Leonid Bunimovich is a Soviet and American mathematician, who made fundamental contributions to the theory of Dynamical Systems, Statistical Physics and various applications.
  Bunimovich received his bachelor's degree in 1967, master's degree in 1969 and PhD in 1973 from the University of Moscow. His masters and PhD thesis advisor was Yakov G. Sinai. In 1986 he finally received Doctor of Sciences degree in "Theoretical and Mathematical Physics". Bunimovich is a Regents' Professor of Mathematics at the Georgia Institute of Technology.
  Already his Master's thesis was a breakthrough where it was proved that some classes of quadratic maps of an interval have an absolutely continuous invariant measure and strong stochastic properties [1].
  Bunimovich is mostly known for discovery of a fundamental mechanism of chaos in dynamical systems called the mechanism of defocusing [2]. This discovery came as a striking surprise not only to mathematics but to physics community as well. Physicists could not believe that such phenomenon is possible until they conducted massive numerical experiments.
context_section_description: Leonid Bunimovich (born August 1, 1947) is a Soviet and American mathematician, who made fundamental contributions to the theory of Dynamical Systems, Statistical Physics and various applications.
  Bunimovich received his bachelor's degree in 1967, master's degree in 1969 and PhD in 1973 from the University of Moscow.  His masters and PhD thesis advisor was Yakov G. Sinai. In 1986 (after Perestroika started) he finally received Doctor of Sciences degree in "Theoretical and Mathematical Physics". Bunimovich is a Regents' Professor of Mathematics at the Georgia Institute of Technology.
  Already his Master's thesis was a breakthrough where it was proved that some classes of quadratic maps of an interval have an absolutely continuous invariant measure and strong stochastic properties [1].
  Bunimovich is mostly known for discovery of a fundamental mechanism of chaos in dynamical systems called the mechanism of defocusing [2]. This discovery came as a striking surprise not only to mathematics but to physics community as well. Physicists could not believe that such (physical!) phenomenon is possible (even though mathematical proves were provided) until they conducted massive numerical experiments. The most famous class of chaotic dynamical systems of this type, dynamical billiards are focusing chaotic billiards (e.g., "Bunimovich stadium","Bunimovich flowers", etc.)[3]. Later Bunimovich proved that his mechanism of defocusing works in all dimensions despite of the phenomenon of astigmatism [4]. Bunimovich introduced absolutely focusing mirrors, which is a new notion in geometric optics, and proved that only such mirrors could be focusing parts of chaotic billiards [5]. He also constructed so called Bunimovich mushrooms, which are visual examples of billiards with mixed regular and chaotic dynamics[6]. In many physics labs over the world were built experimental devices in the form of Bunimovich billiards to study various phenomena in classical and quantum physics.
  Although the discovery of defocusing mechanism was just a part of Bunimovich's PhD thesis, he could not find any job after finishing graduate school thanks to anti-Semitic policies in the Soviet Union. Needless  to say that Bunimovich did not work a single day as a Mathematician in the Soviet Union. Moreover, while finally finding a work place he was not allowed to publish mathematical papers for because of refusal of authorities in the places where he worked to officially confirm that his mathematical papers contain no state secrets. Likewise for a long time he could not attend mathematical conferences even in the Soviet Union. By far Bunimovich was not alone being in such position.
  However, even though being trained as a pure mathematician, Bunimovich turned out to be able to work in applications and made essential and again, totally new in spirit, advances in biomedical studies and in oceanology.
  Notably, Bunimovich introduced and investigated hierarchical models of human populations [7], which allowed to clarify laws of distribution of hereditary diseases and explain data on migration in industrial parts of developed countries. He realized and demonstrated that the lengths of remissions in schizophrenia form a Markov process, i.e. that a length of remission depends only upon the length of the previous remission.  Besides he demonstrated that among the types of attacks in schizophrenia there are those which more (or less) likely to occur after the other types of attacks [8]. Before it was just known that the same type of attack will basically always happen.
  Bunimovich discovered traps for internal waves in non-homogeneous stratified fluids and analyzed their dynamics in such traps which in particular allowed to explain some surprising observations on internal waves in the oceans [9].
  One of the most fundamental problems in Statistical Physics is to derive Deterministic time-irreversible macro-dynamics from deterministic time-reversible Newtonian micro-dynamics. This problem, which was considered before to be mathematically non-tractable was settled in the paper [10] by
caption: Leonid Bunimovich in 1981
  (photo from MFO)
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