Estimation of instability times in Hamiltonian systems: a Shannon entropy approach

PABLO CINCOTTA; CLAUDIA GIORDANO; CRISTIAN BEAUGÉ; RAPHAEL ALVES SILVA

Sochi

Simposio; Dynamical Systems of Classical and Celestial Mechanics; 2022

Steklov Mathematical Institute of Russian Academy of Sciences

In this talk 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 withchaotic motion. After a review of the theory behind this approach, two particular applications arepresented; a 4D symplectic map that models the dynamics around a double resonance and anexoplanetary system approximated by the Three Body Problem. Successful results are obtained for instability time-scales when compared with direct long range integrations (N-body or just iterations).