Intrinsic ergodicity of smooth interval maps
- Cite this article as:
- Buzzi, J. Isr. J. Math. (1997) 100: 125. doi:10.1007/BF02773637
- 248 Downloads
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.