Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2015, Volume 11, Number 3, Pages 475–485 (Mi nd491)  

Original papers

Estimating dimensions of chaotic attractors using Poincaré recurrences

Ya. I. Boev, G. I. Strelkova, V. S. Anishchenko

International Institute of Nonlinear Dynamics Saratov State University, 410026, Russia, Saratov, 83 Astrakhanskaya st.
References:
Abstract: The local theory of Poincaré recurrences is applied to estimate pointwise and information dimensions of chaotic attractors in two-dimensional nonhyperbolic and hyperbolic maps. It is shown that the local pointwise dimension can be defined by calculating the mean recurrence times depending on the return vicinity size. The values of pointwise, information, capacity, and Lyapunov dimensions are compared. It is also analyzed how the structure of attractors can affect the calculation of the dimensions.
Keywords: Poincaré recurrence, probability measure, fractal dimension.
Received: 06.04.2015
Revised: 29.07.2015
Document Type: Article
UDC: 530.182
MSC: 37B20
Language: Russian
Citation: Ya. I. Boev, G. I. Strelkova, V. S. Anishchenko, “Estimating dimensions of chaotic attractors using Poincaré recurrences”, Nelin. Dinam., 11:3 (2015), 475–485
Citation in format AMSBIB
\Bibitem{BoeStrAni15}
\by Ya.~I.~Boev, G.~I.~Strelkova, V.~S.~Anishchenko
\paper Estimating dimensions of chaotic attractors using Poincaré recurrences
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 3
\pages 475--485
\mathnet{http://mi.mathnet.ru/nd491}
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