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Lyapunov’s direct method in estimates of topological entropy

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Abstract

An upper estimate for the topological entropy of a dynamical system defined by a system of ODE is obtained. The estimate involves the Lyapunov functions and Losinskii’s logarithmic norm. The proof uses the known fact that the topological entropy of a mapping acting in a compact space K can be estimated via the fractal dimension of K. Bibliography: 28 titles.

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Authors
  1. V. A. Boichenko
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  2. G. A. Leonov
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 62–75.

Translated by V. A. Boichenko and G. A. Leonov.

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Boichenko, V.A., Leonov, G.A. Lyapunov’s direct method in estimates of topological entropy. J Math Sci 91, 3370–3379 (1998). https://doi.org/10.1007/BF02434914

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  • DOI: https://doi.org/10.1007/BF02434914

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