Anatole Katok

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Anatole Katok (2013)
Svetlana and Anatole Katok, Oberwolfach 2009

Anatole Boris Katok (born August 9, 1944 in Washington, DC , † April 30, 2018 in Danville , Pennsylvania ) was an American mathematician with Russian roots. Katok was the director of the Center for Dynamics and Geometry at Pennsylvania State University . His main research field was the theory of dynamic systems , especially the ergodic theory .

life and work

Katok completed his studies at the renowned Lomonosov University , from which he received his diploma in 1965 and his doctorate in 1968 (with the dissertation Applications of the Method of Approximation of Dynamical Systems by Periodic Transformations to Ergodic Theory bei Sinai ).

After 1978 he taught in the USA. He has taught at three American mathematics chairs: University of Maryland (1978–1984), California Institute of Technology (1984–1990) and, since 1990, at Pennsylvania State University, where he has held the Raymond N. Shibley Professorship since 1996 .

Katok found with Elon Lindenstrauss and Manfred Einsiedler partial results for the Littlewood conjecture in the theory of Diophantine approximations.

He was married to the mathematician Svetlana Katok , who also works on dynamic systems and is involved with Anatole Katok in the MASS project for undergraduate students at Penn State.

His book A first course in Dynamics , written together with his student Boris Hasselblatt , is one of the standard works on dynamic systems.

In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw (Nonuniform hyperbolicity and structure of smooth dynamical systems). He was a Fellow of the American Mathematical Society and, from 2004, the American Academy of Arts and Sciences .

Fonts (selection)

  • with Dmitri Anosow : New examples in smooth ergodic theory. Ergodic diffeomorphisms. (Russian) Trudy Moskov. Mat. Obšč. 1970, 23: 3-36. (English translation: Trans. Moscow Math. Soc. 23 (1970), 1-35.)
  • with AM Stepin: Approximations in ergodic theory. (Russian) Uspehi Mat. Nauk 22 1967 no. 5 (137), 81-106.
  • with AN Zemlyakov: Topological transitivity of billiards in polygons. (Russian) Mat. Zametki 18 (1975), no. 2, 291-300. (English translation: Math Notes 18 (1975), no. 1–2, 760–764 (1976).)
  • Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Inst. Hautes Études Sci. Publ. Math. No. 51: 137-173 (1980).
  • with Jean-Marie Strelcyn, François Ledrappier , Feliks Przytycki : Invariant manifolds, entropy and billiards; smooth maps with singularities. Lecture Notes in Mathematics, 1222. Springer-Verlag, Berlin, 1986. ISBN 3-540-17190-8
  • with Steven Hurder : Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Inst. Hautes Études Sci. Publ. Math. No. 72: 5-61 (1991) (1990).
  • with Ralf Spatzier : First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Inst. Hautes Études Sci. Publ. Math. No. 1994, 79: 131-156.
  • with Hasselblatt: Introduction to the modern theory of dynamical systems. With a supplementary chapter by Katok and Leonardo Mendoza. Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge, 1995. ISBN 0-521-34187-6
  • mit Spatzier: Invariant measures for higher-rank hyperbolic abelian actions. Ergodic Theory Dynam. Systems 16 (1996) no. 4, 751-778.
  • mit Spatzier: Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions. (Russian) Tr. Mat. Inst. Steklova 216 (1997), Din. S is. i Smezhnye Vopr., 292-319. (English translation: Proc. Steklov Inst. Math. 1997, no. 1 (216), 287-314)
  • with Hasselblatt: A first course in dynamics. With a panorama of recent developments. Cambridge University Press, New York, 2003. ISBN 0-521-58304-7 ; 0-521-58750-6
  • with Manfred Einsiedler , Elon Lindenstrauss : Invariant measures and the set of exceptions to Littlewood's conjecture. Ann. of Math. (2) 164 (2006) no. 2, 513-560.
  • with Danijela Damjanović : Local rigidity of partially hyperbolic actions I. KAM method and Z k actions on the torus. Ann. of Math. (2) 172 (2010), no. 3, 1805-1858.

literature

  • Boris Hasselblatt: Anatole Katok - a half-century of dynamics, Notices AMS, May 2019

References

  1. ^ Obituary from legacy.com, accessed May 2, 2018
  2. ^ Center for Dynamics and Geometry
  3. ^ A. Venkatesh: The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture , Bull. AMS 45 (2008), 117-134.
personal data
SURNAME Katok, Anatole
ALTERNATIVE NAMES Katok, Anatole Boris (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH August 9, 1944
PLACE OF BIRTH Washington, DC
DATE OF DEATH April 30, 2018
Place of death Danville , Pennsylvania