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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/11449/76024
Title: 
A rescaling of the phase space for Hamiltonian map: Applications on the Kepler map and mappings with diverging angles in the limit of vanishing action
Author(s): 
Institution: 
  • Universidade Estadual Paulista (UNESP)
  • Abdus Salam ICTP
ISSN: 
0096-3003
Abstract: 
A rescale of the phase space for a family of two-dimensional, nonlinear Hamiltonian mappings was made by using the location of the first invariant Kolmogorov-Arnold-Moser (KAM) curve. Average properties of the phase space are shown to be scaling invariant and with different scaling times. Specific values of the control parameters are used to recover the Kepler map and the mapping that describes a particle in a wave packet for the relativistic motion. The phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant KAM curves whose position of the first of them depends on the control parameters. The transition from local to global chaos is used to estimate the position of the first invariant KAM curve, leading us to confirm that the chaotic sea is scaling invariant. The different scaling times are shown to be dependent on the initial conditions. The universality classes for the Kepler map and mappings with diverging angles in the limit of vanishing action are defined. © 2013 Published by Elsevier Inc. All rights reserved.
Issue Date: 
23-Jul-2013
Citation: 
Applied Mathematics and Computation, v. 221, p. 32-39.
Time Duration: 
32-39
Keywords: 
  • Chaotic sea
  • Invariant
  • KAM curve
  • Kepler map
  • Universality classes
  • Wave packet
  • Control parameters
  • First invariants
  • Initial conditions
  • Specific values
  • Universality class
  • Mapping
  • Phase space methods
  • Wave packets
  • Hamiltonians
Source: 
http://dx.doi.org/10.1016/j.amc.2013.06.045
URI: 
Access Rights: 
Acesso restrito
Type: 
outro
Source:
http://repositorio.unesp.br/handle/11449/76024
Appears in Collections:Artigos, TCCs, Teses e Dissertações da Unesp

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