Recent advances in open billiards with some open problems

Details Recent advances in open billiards with some open problems Recent advances in open billiards with some open problems

2010-07-23

arxiv.org/abs/1007.4166v1

Nonlinear Sciences

Chaotic Dynamics

16 pages, 1 figure in six parts. To appear in Frontiers in the study of chaotic dynamical systems with open problems (Ed. Z. E

Scientific paper

Much recent interest has focused on "open" dynamical systems, in which a classical map or flow is considered only until the trajectory reaches a "hole", at which the dynamics is no longer considered. Here we consider questions pertaining to the survival probability as a function of time, given an initial measure on phase space. We focus on the case of billiard dynamics, namely that of a point particle moving with constant velocity except for mirror-like reflections at the boundary, and give a number of recent results, physical applications and open problems.

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