Poincaré Recurrences in Ergodic Systems Without Mixing

  • Vadim Anishchenko
  • Nadezhda Semenova
  • Elena Rybalova
  • Galina Strelkova
Chapter

Abstract

We study numerically the statistics of recurrences in ergodic sets of the circle map type by using the multifractality analysis. We consider the standard circle map as well as the sets generated in stroboscopic sections of phase trajectories in a nonautonomous van der Pol oscillator and in a harmonically driven conservative nonlinear oscillator. The universal properties of the recurrence time dependence on the size of a return region are established. The numerical results demonstrate a full correspondence with the theoretical data obtained by Valentin Afraimovich.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Vadim Anishchenko
    • 1
  • Nadezhda Semenova
    • 1
  • Elena Rybalova
    • 1
  • Galina Strelkova
    • 1
  1. 1.Saratov State UniversitySaratovRussia

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