Lifting measures to Markov extensions
- Cite this article as:
- Keller, G. Monatshefte für Mathematik (1989) 108: 183. doi:10.1007/BF01308670
IfT is anS-unimodal map with an attracting invariant Cantor set, then ∫log|T′|dμ=0 for the unique invariant measure μ on the Cantor set.
IfT is piecewise invertible, iff is the Radon-Nikodym derivative ofT with respect to a σ-finite measurem, if logf has bounded distortion underT, and if μ is an ergodicT-invariant measure satisfying a certain lower estimate for its entropy, then μ≪m iffhμ (T)=Σlogf dμ.