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Nelin. Dinam., 2014, Volume 10, Number 1, Pages 3–16 (Mi nd421)  

Statistics of Poincaré recurrences in nonautonomous chaotic 1D map

Yaroslav I. Boev, Nadezhda I. Birukova, Vadim S. Anishchenko

International Research Institute of Nonlinear Dynamics, Saratov State University, Astrakhanskaya 83, Saratov, 410026, Russia

Abstract: The statistics of Poincaré recurrences is studied numerically in a one-dimensional cubic map in the presence of harmonic and noisy excitations. It is shown that the distribution density of Poincaré recurrences is periodically modulated by the harmonic forcing. It is substantiated that the theory of the Afraimovich–Pesin dimension can be applied to a nonautonomous map for both harmonic and noisy forcings. It is demonstrated that the relationship between the AP-dimension and Lyapunov exponents is violated in the nonautonomous system.

Keywords: Poincaré recurrence, probability measure, Afraimovich–Pesin dimension.

Full text: PDF file (1174 kB)
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UDC: 530.182
MSC: 37B20
Received: 14.01.2014
Revised: 24.01.2014

Citation: Yaroslav I. Boev, Nadezhda I. Birukova, Vadim S. Anishchenko, “Statistics of Poincaré recurrences in nonautonomous chaotic 1D map”, Nelin. Dinam., 10:1 (2014), 3–16

Citation in format AMSBIB
\Bibitem{BoeBirAni14}
\by Yaroslav~I.~Boev, Nadezhda~I.~Birukova, Vadim~S.~Anishchenko
\paper Statistics of Poincar\'e recurrences in nonautonomous chaotic 1D map
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 1
\pages 3--16
\mathnet{http://mi.mathnet.ru/nd421}


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