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Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors

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Abstract

This paper surveys results of the authors and others conceming estimates for the Hausdorff dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and Rössler systems. A key idea is the interpretation of Hausdorff measure as an analogue of a Lyapunov function.

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  1. St. Petersburg University, Saint Petersburg, Russia

    G. A. Leonov & V. A. Boichenko

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Leonov, G.A., Boichenko, V.A. Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors. Acta Appl Math 26, 1–60 (1992). https://doi.org/10.1007/BF00046607

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