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An inequality for the Ljapunov exponent of an ergodic invariant measure for a piecewise monotonic map of the interval

Chapter 4: Deterministic Dynamical Systems

Part of the Lecture Notes in Mathematics book series (LNM,volume 1486)

Abstract

We consider a piecewise monotonic and piecewise continuous map T on the interval. Under a weak condition on the derivative of T, we show for an ergodic invariant probability measure μ that h μ≤max{0, λμ}, where h μ denotes the entropy and λμ the Ljapunov exponent of μ.

Keywords

  • Pairwise Disjoint
  • Hausdorff Dimension
  • Inverse Image
  • Countable Family
  • Onesided Limit

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. F. Hofbauer, P. Raith: The Hausdorff dimension of an ergodic invariant measure for a piecewise monotonic map of the interval. Can. Math. Bull. (1991)

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  2. G. Keller: Lifting measures to Markov extensions. Mh. Math. 108 (1989), 183–200.

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  3. W. Parry: Topics in Ergodic theory. Cambridge Tracts in Math. 75. Cambridge: Cambridge Univ. Press 1981.

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  4. D. Ruelle: An inequality for the entropy of differentiable maps. Bol. Soc. Bras. Mat. 9 (1978), 83–87.

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© 1991 Springer-Verlag

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Hofbauer, F. (1991). An inequality for the Ljapunov exponent of an ergodic invariant measure for a piecewise monotonic map of the interval. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086672

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  • DOI: https://doi.org/10.1007/BFb0086672

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54662-7

  • Online ISBN: 978-3-540-46431-0

  • eBook Packages: Springer Book Archive