Global transport in a nonautonomous periodic standard map
Abstract
A nonautonomous 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 periodone 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:

 IIMASUNAM (Mexico)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 OSTI Identifier:
 1412059
 Alternate Identifier(s):
 OSTI ID: 1415685
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Communications in Nonlinear Science and Numerical Simulation
 Additional Journal Information:
 Journal Volume: 51; Journal Issue: C; Journal ID: ISSN 10075704
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 58 GEOSCIENCES
Citation Formats
Calleja, Renato C., delCastilloNegrete, D., MartinezdelRio, D., and Olvera, Arturo. Global transport in a nonautonomous periodic standard map. United States: N. p., 2017.
Web. doi:10.1016/j.cnsns.2017.04.004.
Calleja, Renato C., delCastilloNegrete, D., MartinezdelRio, D., & Olvera, Arturo. Global transport in a nonautonomous periodic standard map. United States. doi:10.1016/j.cnsns.2017.04.004.
Calleja, Renato C., delCastilloNegrete, D., MartinezdelRio, D., and Olvera, Arturo. Fri .
"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 delCastilloNegrete, D. and MartinezdelRio, D. and Olvera, Arturo},
abstractNote = {A nonautonomous 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 periodone 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}
}