Using integrability to produce chaos: Billiards with positive entropy
From MaRDI portal
Publication:1181842
DOI10.1007/BF02101504zbMath0744.58041MaRDI QIDQ1181842
Publication date: 27 June 1992
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Ergodic theory (37A99)
Related Items (43)
Convex billiards on convex spheres ⋮ Non-uniformly hyperbolic billiards ⋮ Entropy of non-uniformly hyperbolic plane billiards ⋮ Track billiards ⋮ A Franks' lemma for convex planar billiards ⋮ On another edge of defocusing: hyperbolicity of asymmetric lemon billiards ⋮ Design of hyperbolic billiards ⋮ Semi-focusing billiards: Hyperbolicity ⋮ Chaotic properties of the elliptical stadium ⋮ Singular sets of planar hyperbolic billiards are regular ⋮ On the mathematical transport theory in microporous media: the billiard approach ⋮ Stability and ergodicity of moon billiards ⋮ Hyperbolicity and abundance of elliptical islands in annular billiards ⋮ Polygonal Billiards with Strongly Contractive Reflection Laws: A Review of Some Hyperbolic Properties ⋮ Bernoulli property for some hyperbolic billiards ⋮ Mechanisms of chaos in billiards: dispersing, defocusing and nothing else ⋮ Linearly stable orbits in 3 dimensional billiards ⋮ A lower bound for chaos on the elliptical stadium ⋮ Criterion of absolute focusing for focusing component of billiards ⋮ Regularity of Bunimovich's stadia ⋮ Hyperbolicity of asymmetric lemon billiards * ⋮ Estimates for correlations in billiards with large arcs ⋮ Hyperbolic billiards with nearly flat focusing boundaries. I. ⋮ On the \(K\)-property of some planar hyperbolic billiards ⋮ On the Bernoulli property of planar hyperbolic billiards ⋮ Chaotic dynamics of the elliptical stadium billiard in the full parameter space ⋮ Focusing components in typical chaotic billiards should be absolutely focusing ⋮ Chaotic properties of the truncated elliptical billiards ⋮ Ergodicity of the generalized lemon billiards ⋮ Creating transverse homoclinic connections in planar billiards ⋮ Hard chaos in magnetic billiards (on the hyperbolic plane) ⋮ Semi-focusing billiards: ergodicity ⋮ Elliptic islands in generalized Sinai billiards ⋮ On statistical properties of hyperbolic systems with singularities ⋮ Entropy, Lyapunov exponents, and mean free path for billiards ⋮ Book Review: Chaotic billiards ⋮ A local ergodic theorem for non-uniformly hyperbolic symplectic maps with singularities ⋮ Perturbations of elliptic billiards ⋮ Static and time-dependent perturbations of the classical elliptical billiard. ⋮ Numerical exploration of a family of strictly convex billiards with boundary of class \(C^ 2\). ⋮ Elliptic flowers: simply connected billiard tables where chaotic (non-chaotic) flows move around chaotic (non-chaotic) cores ⋮ Rigorous bounds on Lyapunov exponents of linked twist maps ⋮ Billiards in the \(l^p\) unit balls of the plane.
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A ``transversal fundamental theorem for semi-dispersing billiards
- A theorem on ergodicity of two-dimensional hyperbolic billiards
- Converse KAM: theory and practice
- Principles for the design of billiards with nonvanishing Lyapunov exponents
- Billiards with Pesin region of measure one
- An exhaustive criterion for the non-existence of invariant circles for area-preserving twist maps
- On the ergodic properties of nowhere dispersing billiards
- Instability of the boundary in the billiard ball problem
- Many-dimensional nowhere dispersing billiards with chaotic behavior
- Glancing billiards
- Non-existence of invariant circles
- Invariant families of cones and Lyapunov exponents
- Geodesic flow on the two-sphere, Part I: Positive measure entropy
- Curvature Bounds for the Entropy of the Geodesic Flow on a Surface
- CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
- THE EXISTENCE OF CAUSTICS FOR A BILLIARD PROBLEM IN A CONVEX DOMAIN
- Dynamical systems with elastic reflections
- Riemannian geometry
This page was built for publication: Using integrability to produce chaos: Billiards with positive entropy
