Isentropic perturbations of a chaotic domain

Abstract

Three major properties of the chaotic dynamics of the standard map, namely, the measure \mu of the main connected chaotic domain, the maximum Lyapunov exponent L of the motion in this domain, and the dynamical entropy h = \mu L are studied as functions of the stochasticity parameter K. The perturbations of the domain due to emergence and disintegration of islands of stability, upon small variations of K, are considered in particular. By means of extensive numerical experiments, it is shown that these perturbations are isentropic (at least approximately). In other words, the dynamical entropy does not fluctuate, while local jumps in \mu and L are significant.