Journal
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
Volume 130, Issue 5, Pages -Publisher
SPRINGER
DOI: 10.1007/s10569-018-9832-x
Keywords
Chaotic diffusion; Multidimensional dynamical systems; Entropy; Rate of diffusion
Funding
- Consejo Nacional de Investigaciones Cientificas y Tecnicas de la Republica Argentina (CONICET)
- Universidad Nacional de La Plata
- Instituto de Astrofisica de La Plata
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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.
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