Lyapunov exponents and Kolmogorov-Sinai entropy for a high-dimensional convex billiard

Abstract

We compute the Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a self-bound N-body system that is realized as a convex billiard. This system exhibits truly high-dimensional chaos, and 2N-4 Lyapunov exponents are found to be positive. The KS entropy increases linearly with the numbers of particles. We examine the chaos generating defocusing mechanism and investigate how high-dimensional chaos develops in this system with no dispersing elements.

7 pages, 3 EPS-figures, uses psfig.sty

References in corpus (4)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Largest Lyapunov Exponent for Many Particle Systems at Low Densities
• Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula
• Quantization of a billiard model for interacting particles

Cited by in corpus (4)

• Numerical study of a three-dimensional generalized stadium billiard
• 3D billiards: visualization of regular structures and trapping of chaotic trajectories
• Stable and unstable regimes in higher-dimensional convex billiards with cylindrical shape
• Chaos in cylindrical stadium billiards via a generic nonlinear mechanism