Colloque des sciences mathématiques du Québec

10 octobre 2008 de 16 h 00 à 18 h 00 (heure de Montréal/Miami) Sur place

Visual Chaos: Dispersing, Defocusing, Absolute Focusing and Astigmatism

Colloque par Leonid Bunimovich (Georgia Institute of Technology)

The mechanisms generating chaotic (hyperbolic) behavior in billiards will be discussed. It turned out that all focusing components of the boundary of chaotic billiards should be absolutely focusing. Absolute focusing seems to be a new notion in the geometric optics. The astigmatism comes into play in dimensions greater than two which forces to reduce the sizes of focusing components of chaotic billiard tables. We conclude with the simple visual examples of billiards with divided phase space where any number of chaotic ergodic components coexist with any number of integrable islands.


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