Linearly stable orbits in 3 dimensional billiards
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We construct linearly stable periodic orbits in a class of billiard systems in 3 dimensional domains with boundaries containing semispheres arbitrarily far apart. It shows that the results about planar billiard systems in domains with convex boundaries which have nonvanishing Lyapunov exponents cannot be easily extended to 3 dimensions.
KeywordsNeural Network Statistical Physic Complex System Periodic Orbit Nonlinear Dynamics
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- [A] Arnold, V. I.: Mathematical methods of classical mechanics. Appendix 8. Berlin, Heidelberg, New York: Springer 1978Google Scholar
- [B2] Bunimovich, L. A.: On stochastic dynamics of rays in resonators. Radiofizika28, 1601–1602 (1982)Google Scholar
- [B3] Bunimovich, L. A.: Many-dimensional nowhere despersing billiards with chaotic behavior. Physica D33, 58–64 (1988)Google Scholar
- [B4] Bunimovich, L. A.: Private communicationGoogle Scholar
- [D] Donnay, V. J.: Convex billiards with positive entropy (in preparation)Google Scholar
- [D-L] Donnay, V. J., Liverani, C.: Ergodic properties of particle motion in potential fields (in preparation)Google Scholar
- [S] Sinai, Ya. G.: Dynamical systems with elastic reflections. Russ. Math. Surveys25, 137–189 (1970)Google Scholar
- [C-S] Chernov, N. I., Sinai, Ya. G.: Ergodic properties of some systems of 2-dimensional discs and 3-dimensional spheres. Russ. Math. Surveys42, 181–207 (1987)Google Scholar
- [W2] Wojtkowski, M. P.: Measure theoretic entropy of the system of hard spheres. Erg. Th. Dyn. Syst.8, 133–153 (1988)Google Scholar