Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Av.24A, 1515, Bela Vista, 13506-700, Rio Claro, SP, Brazil
Copyright © 2009 Edson D. Leonel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.