Characterization of chaotic diffusion: a Shannon entropy approach

CINCOTTA, PABLO M

Punta del Este

Simposio; Dynamics Days Latin America and the Caribbean; 2018

Universidad de la República

In the present talk I will discuss two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical argumentsI 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. In the limiting case of near ergodicity, after an appropriate normalization, $S'$ coincides with the expected homogeneous diffusion coefficient.Applications to 4D symplectic maps and the Arnold Hamiltonian will be addressed. Also I will briefly show that the Shannon entropy is also very useful to investigate phase correlations, in particular to unveil strong correlations in the time evolution of the phases involved in the Arnold's Hamiltonian that lead to anomalous diffusion. In this direction, I discuss the validity of several approximations and assumptions usuallyintroduced to derive a local diffusion coefficient in multidimensional near-integrable Hamiltonian systems, in particular the so-called reduced stochasticity approximation.