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Intrinsic ergodicity of smooth interval maps

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Abstract

We generalize the technique of Markov Extension, introduced by F. Hofbauer [10] for piecewise monotonic maps, to arbitrary smooth interval maps. We also use A. M. Blokh’s [1] Spectral Decomposition, and a strengthened version of Y. Yomdin’s [23] and S. E. Newhouse’s [14] results on differentiable mappings and local entropy.

In this way, we reduce the study ofC r interval maps to the consideration of a finite number of irreducible topological Markov chains, after discarding a small entropy set. For example, we show thatC ∞ maps have the same properties, with respect to intrinsic ergodicity, as have piecewise monotonic maps.

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  1. Département de Mathématiques, Université Paris-Sud, 91405, Orsay, France

    Jérôme Buzzi

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  1. Jérôme Buzzi
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Correspondence to Jérôme Buzzi.

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Buzzi, J. Intrinsic ergodicity of smooth interval maps. Isr. J. Math. 100, 125–161 (1997). https://doi.org/10.1007/BF02773637

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  • DOI: https://doi.org/10.1007/BF02773637

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