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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


How the Minimal Poincaré Return Time Depends on the Size of a Return Region in a Linear Circle Map

Discontinuity, Nonlinearity, and Complexity 5(4) (2016) 355--364 | DOI:10.5890/DNC.2016.12.002

N. Semenova; E. Rybalova; V. Anishchenko

Saratov State University, Saratov, 410012, Russia

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Abstract

It is found that the step function of dependence of the minimal Poincaré return time on the size of a return region τinf(ε) for the linear circle map with an arbitrary rotation number can be approximated analytically. All analytical results are confirmed by numerical simulation.

Acknowledgments

This work was partly supported by the RFBR (Grant No. 15-02-02288).

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