Lifting measures to Markov extensions

Keller G (1989)

Publication Type: Journal article, Original article

Publication year: 1989

Journal

Monatshefte für Mathematik Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 108

Pages Range: 183--200

Journal Issue: 2-3

DOI: 10.1007/BF01308670

Abstract

Generalizing a theorem ofHofbauer (1979), we give conditions under which invariant measures for piecewise invertible dynamical systems can be lifted to Markov extensions. Using these results we prove:

  1. (1)

    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.

     
  2. (2)

    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 iffh μ (T)=Σlogf dμ.

 

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

How to cite

APA:

Keller, G. (1989). Lifting measures to Markov extensions. Monatshefte für Mathematik, 108(2-3), 183--200. https://dx.doi.org/10.1007/BF01308670

MLA:

Keller, Gerhard. "Lifting measures to Markov extensions." Monatshefte für Mathematik 108.2-3 (1989): 183--200.

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