Fast numerical test of hyperbolic chaos

Abstract

An effective numerical method for testing the hyperbolicity of chaotic dynamics is suggested. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a distribution of a characteristic value which is bounded within the unit interval and whose zero indicates a tangency between expanding and contracting subspaces. To perform the test one has to solve several copies of equations for infinitesimal perturbations whose number is equal to the sum of numbers of positive and zero Lyapunov exponents. Since this number is normally much less than the full phase space dimension, this method provides a fast and memory saving way for numerical hyperbolicity testing.