Lyapunov exponents in fundamental models of nonlinear resonance

Abstract

The problem of analytical estimation of the Lyapunov exponents and Lyapunov timescales of the motion in multiplets of interacting nonlinear resonances is considered. To this end, we elaborate a unified framework, based on the separatrix map theory, which incorporates both an earlier approach for the first fundamental model of perturbed resonance (given by the perturbed pendulum Hamiltonian) and a new one for its second fundamental model (given by the perturbed Andoyer Hamiltonian). Within this framework, new accurate estimates for the Lyapunov timescales of the inner and outer subsystems of the Solar planetary system are presented and discussed.