Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents


Autoria(s): Leonel, Edson Denis
Contribuinte(s)

Universidade Estadual Paulista (UNESP)

Data(s)

30/09/2013

20/05/2014

30/09/2013

20/05/2014

01/01/2009

Resumo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map. Copyright (C) 2009 Edson D. Leonel.

Formato

22

Identificador

http://dx.doi.org/10.1155/2009/367921

Mathematical Problems In Engineering. New York: Hindawi Publishing Corporation, p. 22, 2009.

1024-123X

http://hdl.handle.net/11449/24944

10.1155/2009/367921

WOS:000271739500001

WOS000271739500001.pdf

Idioma(s)

eng

Publicador

Hindawi Publishing Corporation

Relação

Mathematical Problems in Engineering

Direitos

openAccess

Tipo

info:eu-repo/semantics/article