Statistical properties of Poincaré recurrences and Afraimovich-Pesin dimension for the circle map

DOI10.1016/J.CNSNS.2014.08.037zbMath1329.37043OpenAlexW2049287266MaRDI QIDQ907669

Nadezhda I. Semenova, Vadim S. Anishchenko, Tatiana E. Vadivasova, Galina I. Strelkova

Publication date: 26 January 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2014.08.037

zbMATH Keywords

Poincaré recurrencescircle mapAfraimovich-Pesin dimensionDiophantine and Liouvillian numbers

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (3)

Fibonacci stairs and the Afraimovich-Pesin dimension for a stroboscopic section of a nonautonomous van der Pol oscillator ⋮ Poincaré Recurrences in Ergodic Systems Without Mixing ⋮ Local and global approaches to the problem of Poincaré recurrences. Applications in nonlinear dynamics

Cites Work

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• Statistics of Poincaré recurrences in local and global approaches
• Statistics of Poincaré recurrences for a class of smooth circle maps
• Statistics of return times: A general framework and new applications
• Pesin’s dimension for Poincaré recurrences
• FRACTAL DIMENSION FOR POINCARÉ RECURRENCES AS AN INDICATOR OF SYNCHRONIZED CHAOTIC REGIMES
• On the notion of recurrence in discrete stochastic processes
• Rational approximations to algebraic numbers
• Statistical characteristics of the Poincaré return times for a one-dimensional nonhyperbolic map

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