Markov extensions and lifting measures for complex polynomials
نویسنده
چکیده
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 δ-conformal measure is liftable if and only if the set of points with positive Lyapunov exponent has positive measure.
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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 canon-ical 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 po...
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