Estimating dimensions of chaotic attractors using Poincaré recurrences

    Received 06 April 2015

    2015, Vol. 11, No. 3, pp.  475-485

    Author(s): Boev Y. I., Strelkova G. I., Anishchenko V. S.

    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
    Citation: Boev Y. I., Strelkova G. I., Anishchenko V. S., Estimating dimensions of chaotic attractors using Poincaré recurrences, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 3, pp.  475-485

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