Ergodic property of a Henon-Heiles model with reflecting walls

摘要

A modified Henon-Heiles model with reflecting walls is suggested to discuss the ergodic property of the motion of a two-dimensional oscillator with nonlinear coupling. A quantitative method for estimating the ergodicity of a chaotic trajectory is proposed in terms of a microcanonical distribution. The influence of the boundary on the ergodic and chaotic behavior is discussed. Our investigations show that, by adjusting the distance and the shape of the boundary, a simple Henon-Heiles system can reach ergodicity on the constant-energy surface, and therefore various concepts in traditional statistical physics can be introduced into this simple system.