The Shannon entropy: An efficient indicator of dynamical stability

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. (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

This work demonstrates that Shannon entropy is an efficient dynamical indicator that directly measures diffusion rate and provides a time scale for instabilities in chaos. By solving Hamiltonian flow, it eliminates the need for variational equations. Comparative analysis shows that this novel technique offers more dynamical information compared to classical chaos indicators.