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.
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References
F. Hofbauer, P. Raith: The Hausdorff dimension of an ergodic invariant measure for a piecewise monotonic map of the interval. Can. Math. Bull. (1991)
G. Keller: Lifting measures to Markov extensions. Mh. Math. 108 (1989), 183–200.
W. Parry: Topics in Ergodic theory. Cambridge Tracts in Math. 75. Cambridge: Cambridge Univ. Press 1981.
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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