Principles for the design of billiards with nonvanishing Lyapunov exponents

Keywords

Lyapunov exponent, Complex system, Mathematics, Nonlinear system, Lyapunov function

References

• Ergodic theoryManfred Denker, Konrad Jacobs — 1963
• Invariant Manifolds, Entropy and Billiards: Smooth Maps With SingularitiesAnatole Katok, Jean-Marie Strelcyn, François Ledrappier — 1986
• Classical dynamics of a family of billiards with analytic boundariesMarko Robnik — 1983
• THE EXISTENCE OF CAUSTICS FOR A BILLIARD PROBLEM IN A CONVEX DOMAINV. F. Lazutkin — 1973
• Numerical experiments on the free motion of a point mass moving in a plane convex region: Stochastic transition and entropyGiancarlo Benettin, Jean-Marie Strelcyn — 1978
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORYYa. B. Pesin — 1977
• Power-law behavior of Lyapunov exponents in some conservative dynamical systemsGiancarlo Benettin — 1984
• ON A FUNDAMENTAL THEOREM IN THE THEORY OF DISPERSING BILLIARDSL A Bunimovič, Ja. G. Sinaĭ — 1973
• Invariant families of cones and Lyapunov exponentsMaciej P. Wojtkowski — 1985
• A proof of the estimation from below in Pesin's entropy formulaFran ̧ois Ledrappier, Jean-Marie Strelcyn — 1982
• On the ergodic properties of nowhere dispersing billiardsLeonid Bunimovich — 1979
• Dynamical systems with elastic reflectionsYakov G. Sinai — 1970
• Mathematical Methods of Classical MechanicsV. I. Arnold — 1974
• A multiplicative ergodic theorem: Lyapunov characteristic num-bers for dynamical systemsV. I. Oseledec — 1968
• Ergodic TheoryI. P. Cornfeld, Ya. G. Sinaǐ, Sergey Fomin — 1982
• Dynamical systems with elastic reflections. Ergodic properties of dispersing billiardsYa. G. Sinaǐ — 1970

Cited by

• A Case of Hyperbolic BilliardsZak Webb — 2009
• Surface billiards and nonvanishing Lyapunov exponentsCheng Jian — 1997
• Birth of an elliptic island in a chaotic seaCarlangelo Liverani — 2004
• The K-property ofN billiard balls INándor Simányi — 1992
• Semidispersing billiards with an infinite cusp. IIMarco Lenci — 2003
• Billiards with positive topological entropyChristian Foltin — 2002
• Semi-Focusing Billiards: HyperbolicityLeonid Bunimovich, Gianluigi Del Magno — 2006
• Billiards in the lp unit balls of the planeMing‐Jer Jeng, Oliver Knill — 1996
• Power law scaling of the top Lyapunov exponent of a Product of Random MatricesK C Ravishankar — 1989
• Ergodic properties of plane billiards with symmetric potentialsRoberto Markarian — 1992
• Stability in High Dimensional Steep Repelling PotentialsA. N. Rapoport, Vered Rom‐Kedar, Dmitry Turaev — 2008
• The system of two spinning disks in the torusMaciej P. Wojtkowski — 1994
• Ergodicity of a class of truncated elliptical billiardsGianluigi Del Magno — 2001
• Criterion of absolute focusing for focusing component of billiardsLeonid Bunimovich — 2009
• Illumination problem and absolutely focusing mirrorsLeonid Bunimovich — 2001
• Some new results on Robnik billiardsA. Hayli, Th. Dumont, Jean Moulin-Ollagnier — 1987
• Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponentsBruce N. Miller, K. Ravishankar — 1988
• Ergodicity of the generalized lemon billiards.Jingyu Chen, Luke Mohr, Hong-Kun Zhang — 2013
• New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadiumsN. Chernov — 1991
• Ergodicity of classical billiard ballsDomokos Szász — 1993

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