Global dynamics and diffusion in the rational standard map

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 ≤ μ < 1, that breaks the entire character of the perturbing function. By means of analytical and numerical methods it is show...

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Detalles Bibliográficos
Autores principales:	Cincotta, Pablo Miguel, Simó, Carles
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2020
Materias:	Física Astronomía Area preserving maps Rational standard map Global dynamics Chaotic diffusion Shannon entropy
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/134914
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-134914
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Física Astronomía Area preserving maps Rational standard map Global dynamics Chaotic diffusion Shannon entropy
spellingShingle	Física Astronomía Area preserving maps Rational standard map Global dynamics Chaotic diffusion Shannon entropy Cincotta, Pablo Miguel Simó, Carles Global dynamics and diffusion in the rational standard map
topic_facet	Física Astronomía Area preserving maps Rational standard map Global dynamics Chaotic diffusion Shannon entropy
description	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 ≤ μ < 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 μ values. Moreover, for K not small and near suitable values of μ, 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 ≈ 2 π accelerator modes exist for μ less than some critical value but also within very narrow intervals when 0.9 < μ < 1. Big differences for the domains of existence of rotationally invariant curves (much larger, for μ moderate, or much smaller, for μ 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.
format	Articulo Articulo
author	Cincotta, Pablo Miguel Simó, Carles
author_facet	Cincotta, Pablo Miguel Simó, Carles
author_sort	Cincotta, Pablo Miguel
title	Global dynamics and diffusion in the rational standard map
title_short	Global dynamics and diffusion in the rational standard map
title_full	Global dynamics and diffusion in the rational standard map
title_fullStr	Global dynamics and diffusion in the rational standard map
title_full_unstemmed	Global dynamics and diffusion in the rational standard map
title_sort	global dynamics and diffusion in the rational standard map
publishDate	2020
url	http://sedici.unlp.edu.ar/handle/10915/134914
work_keys_str_mv	AT cincottapablomiguel globaldynamicsanddiffusionintherationalstandardmap AT simocarles globaldynamicsanddiffusionintherationalstandardmap
bdutipo_str	Repositorios
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Global dynamics and diffusion in the rational standard map

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