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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Araujo, Vitor Galatolo, Stefano and Pacifico, Maria José 2014. Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives. International Journal of Bifurcation and Chaos, Vol. 24, Issue. 10, p. 1430028.

    Bruin, Henk and Kalle, Charlene 2014. Natural extensions for piecewise affine maps via Hofbauer towers. Monatshefte für Mathematik, Vol. 175, Issue. 1, p. 65.

    Alves, José F. Dias, Carla L. and Luzzatto, Stefano 2013. Geometry of expanding absolutely continuous invariant measures and the liftability problem. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Vol. 30, Issue. 1, p. 101.

    Pinheiro, Vilton 2011. Expanding measures. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Vol. 28, Issue. 6, p. 889.

    PESIN, YA. B. SENTI, S. and ZHANG, K. 2008. Lifting measures to inducing schemes. Ergodic Theory and Dynamical Systems, Vol. 28, Issue. 02,


Markov extensions and lifting measures for complex polynomials

  • HENK BRUIN (a1) and MIKE TODD (a1)
  • DOI:
  • Published online: 12 March 2007

For polynomials $f$ on the complex plane with a dendrite Julia set we study invariant probability measures, obtained from a reference measure. To do this we follow Keller [K1] in constructing canonical Markov extensions. We discuss ‘liftability’ of measures (both $f$-invariant and non-invariant) to the Markov extension, showing that invariant measures are liftable if and only if they have a positive Lyapunov exponent. We also show that $\delta$-conformal measure is liftable if and only if the set of points with positive Lyapunov exponent has positive measure.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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