Periodic orbits in coupled Hénon maps: Lyapunov and multifractal analysis

Abstract

A powerful algorithm is implemented in a 1-d lattice of Hénon maps to extract orbits which are periodic both in space and time. The method automatically yields a suitable symbolic encoding of the dynamics. The arrangement of periodic orbits allows us to elucidate the spatially chaotic structure of the invariant measure. A new family of specific Lyapunov exponents is defined, which estimate the growth rate of spatially inhomogeneous perturbations. The specific exponents are shown to be related to the comoving Lyapunov exponents. Finally, the ζ-function formalism is implemented to analyze the scaling structure of the invariant measure both in space and time.