Domokos Szász: Mathematical billiards and chaos

Abstract:
I intend to explain - for a general audience - some of Sinai’s groundbreaking ideas and their implications for chaotic billiards. No particular background knowledge will be assumed.
Can random behavior arise in purely deterministic systems? By way of responding to that question the theory of hyperbolic dynamical systems made a spectacular progress in the 1960’s. Phenomenologically, being chaotic can be seen as being sensitive to initial conditions, something borne out in nature by the difficulty of forecasting weather or earthquakes, . . . (Sci-fi has dubbed this as the ’butterfly effect’.) To produce a mathematical model of chaotic motion Sinai, in the 60’s, introduced scattering billiards, i. e. those with convex obstacles (like flippers in bingo halls). He also showed that the simplest’ Sinai billiard was ergodic. This opened the way to answering a 1872 hypothesis of the great Austrian physicist Boltzmann, a hypothesis that, in the 1930’s, also led to the birth of ergodic theory. Beyond their mathematical beauty and fruitful interconnections with many branches of mathematics, chaotic billiards are most appropriate models where laws of statistical physics can be verified. A celebrated example is Einstein’s 1905 diffusion equation.
Program for the Abel Lectures 2014
1. "Now everything has been started? The origin of deterministic chaos" by Abel Laureate Yakov Sinai, Princeton University and Landau Institute for Theoretical Physics, Russian Academy of Sciences
2. "Kolmogorov-Sinai entropy and homogeneous dynamics" by Professor Gregory Margulis, Yale University
3. "Between mathematics and physics" by Konstantin Khanin, University of Toronto
4. "Mathematical billiards and chaos" a science lecture by Domokos Szász, Eötvös University, Budapest

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