Recent advances in open billiards with some open problems
Chaotic Dynamics
2016-11-23 v1 Dynamical Systems
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.
Cite
@article{arxiv.1007.4166,
title = {Recent advances in open billiards with some open problems},
author = {Carl P. Dettmann},
journal= {arXiv preprint arXiv:1007.4166},
year = {2016}
}
Comments
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)