Global transport in a nonautonomous periodic standard map

R. C. Calleja; D. del-Castillo-Negrete; D. Martínez-del-Río; A. Olvera

doi:10.1016/j.cnsns.2017.04.004

Global transport in a nonautonomous periodic standard map

R. C. Calleja, D. del-Castillo-Negrete, D. Martínez-del-Río, A. Olvera

Plasma Theory and Modeling

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1 Scopus citations

Abstract

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. The results are contrasted with similar calculations found in the literature.

Original language	English
Pages (from-to)	198-215
Number of pages	18
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	51
DOIs	https://doi.org/10.1016/j.cnsns.2017.04.004
State	Published - Oct 1 2017

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title = "Global transport in a nonautonomous periodic standard map",

abstract = "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. The results are contrasted with similar calculations found in the literature.",

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AU - Calleja, R. C.

AU - del-Castillo-Negrete, D.

AU - Martínez-del-Río, D.

AU - Olvera, A.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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. The results are contrasted with similar calculations found in the literature.

AB - 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. The results are contrasted with similar calculations found in the literature.

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VL - 51

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EP - 215

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

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Global transport in a nonautonomous periodic standard map

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