Markov extensions and lifting measures for complex polynomials

• Autores: Henk Bruin, Mike Todd
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 3, 2007, págs. 743-768
• Idioma: inglés
• DOI: 10.1017/s0143385706000976
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• Resumen

  • 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.