Intrinsic ergodicity of smooth interval maps |
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Authors: | Jérôme Buzzi |
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Institution: | (1) Département de Mathématiques, Université Paris-Sud, 91405 Orsay, France |
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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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Keywords: | |
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