Equilibrium states and Hausdorff measures for interval maps. (English) Zbl 0809.58025
Equilibrium states \(\mu\) for a given piecewise monotone map of an interval and a given function of bounded variation are considered. Let \(\nu\) be Hausdorff measure. The authors give an integral test to check conditions \(\mu \ll \nu\) or \(\mu \perp \nu\). The class of maps considered includes unimodal maps with negative Schwarzian. The paper generalizes previous results for rational maps obtained by M. Denker, F. Przytycki, M. Urbanski, and A. Zdunik.
Reviewer: Yu.Latushkin (Columbia)
MSC:
| 37D35 | Thermodynamic formalism, variational principles, equilibrium states for dynamical systems |
| 37C40 | Smooth ergodic theory, invariant measures for smooth dynamical systems |
| 37E05 | Dynamical systems involving maps of the interval |
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