IALP   13078
INSTITUTO DE ASTROFISICA LA PLATA
Unidad Ejecutora - UE
artículos
Título:
The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
Autor/es:
CINCOTTA, P. M.; GIORDANO, C. M.
Revista:
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
Editorial:
SPRINGER
Referencias:
Año: 2018 vol. 130 p. 1 - 21
ISSN:
0923-2958
Resumen:
In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S´, estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S´ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.