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Topological entropy of a dynamical system on the space of one-dimensional maps

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Nonlinear Oscillations

Abstract

We study properties of the topological entropy of the map F: φ ↦ f ○ φ, φ ∈ C(I), generated by a fixed continuous map f ∈ C(I) of an interval of the straight line. In particular, we show that the topological entropy h(F) > 0 if and only if h(f) > 0.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    S. F. Kolyada

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  1. S. F. Kolyada
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Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 180–187, April–June, 2004.

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Kolyada, S.F. Topological entropy of a dynamical system on the space of one-dimensional maps. Nonlinear Oscill 7, 179–186 (2004). https://doi.org/10.1007/s11072-005-0004-z

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  • DOI: https://doi.org/10.1007/s11072-005-0004-z

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