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Title: Global transport in a nonautonomous periodic standard map

A non-autonomous version of the standard map with a periodic variation of the perturbation parameter is introduced and studied via an autonomous map obtained from the iteration of the nonautonomous map over a period. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers of invariant sets. The role of the nonautonomous dynamics on period-one orbits, stability and bifurcation is studied. The critical boundaries for the global transport and for the destruction of invariant circles with fixed rotation number are studied in detail using direct computation and a continuation method. In the case of global transport, the critical boundary has a particular symmetrical horn shape. Here, the results are contrasted with similar calculations found in the literature.
Authors:
 [1] ;  [2] ;  [1] ;  [1]
  1. IIMAS-UNAM (Mexico)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Communications in Nonlinear Science and Numerical Simulation
Additional Journal Information:
Journal Volume: 51; Journal Issue: C; Journal ID: ISSN 1007-5704
Publisher:
Elsevier
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 58 GEOSCIENCES
OSTI Identifier:
1412059
Alternate Identifier(s):
OSTI ID: 1415685

Calleja, Renato C., del-Castillo-Negrete, D., Martinez-del-Rio, D., and Olvera, Arturo. Global transport in a nonautonomous periodic standard map. United States: N. p., Web. doi:10.1016/j.cnsns.2017.04.004.
Calleja, Renato C., del-Castillo-Negrete, D., Martinez-del-Rio, D., & Olvera, Arturo. Global transport in a nonautonomous periodic standard map. United States. doi:10.1016/j.cnsns.2017.04.004.
Calleja, Renato C., del-Castillo-Negrete, D., Martinez-del-Rio, D., and Olvera, Arturo. 2017. "Global transport in a nonautonomous periodic standard map". United States. doi:10.1016/j.cnsns.2017.04.004. https://www.osti.gov/servlets/purl/1412059.
@article{osti_1412059,
title = {Global transport in a nonautonomous periodic standard map},
author = {Calleja, Renato C. and del-Castillo-Negrete, D. and Martinez-del-Rio, D. and Olvera, Arturo},
abstractNote = {A non-autonomous version of the standard map with a periodic variation of the perturbation parameter is introduced and studied via an autonomous map obtained from the iteration of the nonautonomous map over a period. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers of invariant sets. The role of the nonautonomous dynamics on period-one orbits, stability and bifurcation is studied. The critical boundaries for the global transport and for the destruction of invariant circles with fixed rotation number are studied in detail using direct computation and a continuation method. In the case of global transport, the critical boundary has a particular symmetrical horn shape. Here, the results are contrasted with similar calculations found in the literature.},
doi = {10.1016/j.cnsns.2017.04.004},
journal = {Communications in Nonlinear Science and Numerical Simulation},
number = C,
volume = 51,
place = {United States},
year = {2017},
month = {4}
}