Ju l 2 00 5 MARKOV EXTENSIONS AND LIFTING MEASURES FOR COMPLEX
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 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 positive Lya-punov 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.
منابع مشابه
Markov extensions and lifting measures for complex polynomials
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 positi...
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تاریخ انتشار 2005