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, $$S'$$ S ′ , estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, $$S'$$ 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.
Celestial Mechanics and Dynamical Astronomy – Springer Journals
Published: Apr 28, 2018
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