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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


Dumitru Baleanu (editor)

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


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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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.


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


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