Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
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 paramete...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2009-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2009/367921 |
| Summary: | 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. |
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| ISSN: | 1024-123X 1563-5147 |