Geodesic
Estimating dimensions of chaotic attractors using Poincaré recurrences
Russian journal of nonlinear dynamics, Tome 11 (2015) no. 3, pp. 475-485

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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.
Mots-clés : Poincaré recurrence, fractal dimension.
Keywords: probability measure 
@article{ND_2015_11_3_a2,
     author = {Ya. I. Boev and G. I. Strelkova and V. S. Anishchenko},
     title = {Estimating dimensions of chaotic attractors using {Poincar\'e} recurrences},
     journal = {Russian journal of nonlinear dynamics},
     pages = {475--485},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2015_11_3_a2/}
}
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Ya. I. Boev; G. I. Strelkova; V. S. Anishchenko. Estimating dimensions of chaotic attractors using Poincaré recurrences. Russian journal of nonlinear dynamics, Tome 11 (2015) no. 3, pp. 475-485. http://geodesic.mathdoc.fr/item/ND_2015_11_3_a2/