Supplement to the article "Approximating multi-dimensional Hamiltonian flows by billiards": Proof of C${}^0$ and C${}^r$ - closeness Theorems

Abstract

This supplement to the article "Approximating multi-dimensional Hamiltonian flows by billiards" contains the proofs of C${}^0$ and C${}^r$ - closeness theorems stated in the article.

6 pages, 1 figure

References in corpus (6)

• Proof of the Ergodic Hypothesis for Typical Hard Ball Systems
• Cayley-Type Conditions for Billiards within $k$ Quadrics in $R^d$
• Hard ball systems are completely hyperbolic
• Numerical study of a three-dimensional generalized stadium billiard
• Non-ergodicity of the motion in three dimensional steep repelling dispersing potentials
• Soft billiards with corners

Cited by in corpus (9)

• Soft wall effects on interacting particles in billiards
• 3D billiards: visualization of regular structures and trapping of chaotic trajectories
• A saddle in a corner - a model of collinear triatomic chemical reactions
• Non-ergodicity of the motion in three dimensional steep repelling dispersing potentials
• Smooth Hamiltonian systems with soft impacts
• Three unequal masses on a ring and soft triangular billiards
• Revisiting the Toda-Brumer-Duff criterion for order-chaos transition in dynamical systems
• Stable motions of high energy particles interacting via a repelling potential
• Chaos and Regularity in an Anisotropic Soft Squircle Billiard