Estimation of diffusion time with the Shannon entropy approach

Abstract

The present work revisits and improves the Shannon entropy approach when applied to the estimation ofan instability timescale for chaotic diffusion in multidimensional Hamiltonian systems. This formulation hasalready been proved efficient in deriving the diffusion timescale in 4D symplectic maps and planetary systems,when the diffusion proceeds along the chaotic layers of the resonance’s web. Herein the technique is used toestimate the diffusion rate in the Arnold model, i.e., of the motion along the homoclinic tangle of the so-calledguiding resonance for several values of the perturbation parameter such that the overlap of resonances is almostnegligible. Thus differently from the previous studies, the focus is fixed on deriving a local timescale related tothe speed of an Arnold diffusion-like process. The comparison of the current estimates with determinations ofthe diffusion time obtained by straightforward numerical integration of the equations of motion reveals a quitegood agreement.