Extensive Numerical Results for Integrable Case of Standard Map


TIRNAKLI U. , Tsallis C.

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS, vol.23, no.2, pp.149-152, 2020 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.33581/1561-4085-2020-23-2-149-152
  • Title of Journal : NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
  • Page Numbers: pp.149-152

Abstract

In recent years, conservative dynamical systems have become a vivid area of research from the statistical mechanical characterization viewpoint. With this respect, several area-preserving 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.