Invariant Spectra in N-Coupled Standard Maps

Abstract

This paper examines the evolution of the dynamical spectra of stretching numbers in a system of [Formula: see text]-coupled Standard Maps. It is found that the convergence rate of the spectra to their invariant forms is independent of the dimensionality 2[Formula: see text] and the nonlinearity/coupling parameters. This rate is impressively faster than one could predict on the basis of ergodicity. This effect is probably associated with the manifold of the maximum Lyapunov exponent along which the main stretching occurs. It seems that dynamical spectra depend mainly on the dramatically smaller subspace defined by this unstable manifold.