Intrinsic ergodicity of smooth interval maps
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We generalize the technique of Markov Extension, introduced by F. Hofbauer  for piecewise monotonic maps, to arbitrary smooth interval maps. We also use A. M. Blokh’s  Spectral Decomposition, and a strengthened version of Y. Yomdin’s  and S. E. Newhouse’s  results on differentiable mappings and local entropy.
In this way, we reduce the study ofCr 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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