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 a direct measure of the diffusion rate and thus a time-scale for the instabilities arising when dealing with chaos. Its computation just involves the solution of the Hamiltonian flow, the variational equations are not required. After a review of the theory behind this approach, two particular applications are presented; a 4D symplectic map and the exoplanetary system HD 181433, approximated by the Planar Three Body Problem. Successful results are obtained for instability time-scales when compared with direct long range integrations (N-body or just iterations). Comparative dynamical maps reveal that this novel technique provides much more dynamical information than a classical chaos indicator.