Extensive Numerical Results for Integrable Case of Standard Map
Articles > Article · 2020
Authors: Uğur TIRNAKLI, Constantino Tsallis
Nonlinear Phenomena in Complex Systems, Journal Indexed in AHCI, International, Scopus, 2020, vol 23, pp 149-152
DOI: 10.33581/1561-4085-2020-23-2-149-152
Summary
In recent years, conservative dynamical systems have become a vivid area of research from the statistical mechanical characterization viewpoint. With this respect, several areapreserving maps have been studied. It has been numerically shown that the probability distribution of the sum of the suitable random variable of these systems can be well approximated by a Gaussian (q-Gaussian) when the initial conditions are randomly selected from the chaotic sea (region of stability islands) in the available phase space. In this study, we will summarize these results and discuss a special case for the standard map, a paradigmatic example of area-preserving maps, for which the map is totally integrable.