The Shannon entropy: An efficient indicator of dynamical stability

Abstract

In this work it is shown that the Shannon entropy is an efficient dynamical indicator that provides adirect measure of the diffusion rate and thus a time-scale for the instabilities arising when dealing withchaos. Its computation just involves the solution of the Hamiltonian flow, the variational equationsare not required. After a review of the theory behind this approach, two particular applications arepresented; a 4D symplectic map and the exoplanetary system HD 181433, approximated by the PlanarThree Body Problem. Successful results are obtained for instability time-scales when compared withdirect long range integrations (N-body or just iterations). Comparative dynamical maps reveal that thisnovel technique provides much more dynamical information than a classical chaos indicator.