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On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II

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Abstract

The results about measures with maximal entropy, which are proved in [3], are extended to the following more general class of transformations on the unit intervalI : I=∪ =1/n i Ji, theJ i are disjoint intervals,f/J i is increasing or decreasing and continuous, andh top(f)>0.

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References

  1. R. Bowen,On axiom A diffeomorphism, CBMS Regional Conf. Ser. Math.35, Amer. Math. Soc., Providence, R.I., 1978.

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  2. M. Denker, Ch. Grillenberger and K. Sigmund,Ergodic Theory on Compact Spaces, Lecture Notes in Math.527, Springer-Verlag, Berlin-Heidelberg-New York, 1976.

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  3. F. Hofbauer,On intrinsic ergodicity of piecewise monotonic transformations with positive entropy, Israel J. Math.34 (1979), 213–236.

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  4. F. Hofbauer,Maximal measures for simple piecewise monotonic transformations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete52 (1980), 289–300.

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  1. Mathematisches Institut der Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Franz Hofbauer

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  1. Franz Hofbauer
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Hofbauer, F. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II. Israel J. Math. 38, 107–115 (1981). https://doi.org/10.1007/BF02761854

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  • DOI: https://doi.org/10.1007/BF02761854

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