Recent advances in open billiards with some open problems
arXiv:1007.4166 · doi:10.1142/9789814340700_0011
Abstract
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.
16 pages, 1 figure in six parts. To appear in Frontiers in the study of chaotic dynamical systems with open problems (Ed. Z. Elhadj and J. C. Sprott, World Scientific)
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- Resonances in open quantum maps
- Open Mushrooms: Stickiness revisited
- Metastability of Certain Intermittent Maps
- Dependence of chaotic diffusion on the size and position of holes
- Faster than expected escape for a class of fully chaotic maps
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