WaPo – Anatole Katok, mathematician who explored chaos theory, dies at 73


  • American mathematician, Anatole Katok, a leader in the theoretical exploration of dynamical systems – a subject treating the way complex aspects of the real world change and develop over time, died April 30 at a medical center in Danville, Pa at 73
  • was director of the Center for Dynamics and Geometry at Pennsylvania State University
  • was hailed for revolutionizing the study of dynamical systems through sophisticated mathematics –  Gregory Margulis, a member of the mathematics faculty at Yale University, called him “one of the giants.”
  • his scholarly work ventured into areas embracing chaos theory, symbolized by the “butterfly effect.”
  • At one time, it seemed to scientists that exact prediction was possible for many important natural systems
    • particularly those composed of inanimate particles (e.g., weather)
    • belief was perfect knowledge of the state of the system, and of the rules of interaction prevailing among its components, would allow for perfect forecasts
  • However, the desired degree of precision often proved impossible to obtain
    • evolution of a system could depend with great sensitivity on just the sort of information that could not be precisely obtained 
  • introduced the idea of chaos
    • some systems depend so sensitively on their initial characteristics in one region of the system may induce a major event in another
  • Among Katok’s particular contributions to dynamical-systems theory was the creation of an all-encompassing mathematical framework that shaped and organized results and ways of thinking
    • systems were placed in elliptic, hyperbolic or parabolic categories
  • he was known for work in ergodic theory (https://en.wikipedia.org/wiki/Ergodic_theory)
  • Making use of advanced geometrical concepts, sophisticated spaces or borrowings from physics such as the idea of entropy, Katok built overarching frameworks of abstraction, classification and generality, offering insight and a deeper understanding of dynamical systems
  • Dr. Katok’s collaboration with his former student Boris Hasselblatt resulted in the book “Introduction to the Modern Theory of Dynamical Systems,” considered an encyclopedia of modern dynamical systems and is among the most cited publications in the area

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