Phase correlations in chaotic dynamics: a Shannon entropy measure

CINCOTTA, P. M.; GIORDANO, C.M.

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY

SPRINGER

Lugar: Berlin; Año: 2018 vol. 130

0923-2958

In the present work we introduce two new estimators of chaotic diffusionbased on the Shannon entropy. Using theoretical, heuristic and numerical argumentswe show that the entropy, S, provides a measure of the diffusion extent of a givensmall initial ensemble of orbits, while an indicator related with the time derivativeof the entropy, S 0 , estimates the diffusion rate. We show that in the limiting case ofnear ergodicity, after an appropriate normalization, S 0 coincides with the standardhomogeneous diffusion coefficient. The very first application of this formulationto a 4D symplectic map and to the Arnold Hamiltonian reveals very successful andencouraging results.