Global dynamics and diffusion in the rational standard map

[摘要] In this paper we study the dynamics of the Rational Standard Map, which is a generalization of the Standard Map. It depends on two parameters, the usual K and a new one, 0 <= mu < 1, that breaks the entire character of the perturbing function. By means of analytical and numerical methods it is shown that this system presents significant differences with respect to the classical Standard Map. In particular, for relatively large values of K the integer and semi-integer resonances are stable for some range of mu values. Moreover, for K not small and near suitable values of mu, its dynamics could be assumed to be well represented by a nearly integrable system. On the other hand, periodic solutions or accelerator modes also show differences between this map and the standard one. For instance, in case of K approximate to 2 pi accelerator modes exist for mu less than some critical value but also within very narrow intervals when 0.9 < mu < 1. Big differences for the domains of existence of rotationally invariant curves (much larger, for mu moderate, or much smaller, for mu close to 1 than for the standard map) appear. While anomalies in the diffusion are observed, for large values of the parameters, the system becomes close to an ergodic one. (C) 2020 Elsevier B.V. All rights reserved.

[发布日期] 2020-12-01

[关键词] Area preserving maps;Rational standard map;Global dynamics;Chaotic diffusion;Shannon entropy