Markov extensions and lifting measures for complex polynomials

dc.creatorBruin, Henk
dc.creatorTodd, Mike
dc.date2005-07-26
dc.date2006-10-16
dc.date.accessioned2026-07-07T08:07:07Z
dc.date.available2026-07-07T08:07:07Z
dc.descriptionFor 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 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.
dc.descriptionSome changes have been made, in particular to Sections 2 and 3, to clarify the exposition. Typos have been corrected and references updated
dc.identifierhttps://arxiv.org/abs/math/0507543
dc.identifierhttp://arxiv.org/abs/math/0507543
dc.identifierErgodic Theory Dynam. Systems 27 (2007) 743-768
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130834
dc.subjectDynamical Systems
dc.subject37D25 (Primary); 37F10; 37F35; 37C40 (Secondary)
dc.titleMarkov extensions and lifting measures for complex polynomials
dc.typetext

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