, Volume 100, Issue 1, pp 125-161

Intrinsic ergodicity of smooth interval maps

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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.