Markov extensions and lifting measures for complex polynomials
| dc.creator | Bruin, Henk | |
| dc.creator | Todd, Mike | |
| dc.date | 2005-07-26 | |
| dc.date | 2006-10-16 | |
| dc.date.accessioned | 2026-07-07T08:07:07Z | |
| dc.date.available | 2026-07-07T08:07:07Z | |
| dc.description | 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 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.description | Some changes have been made, in particular to Sections 2 and 3, to clarify the exposition. Typos have been corrected and references updated | |
| dc.identifier | https://arxiv.org/abs/math/0507543 | |
| dc.identifier | http://arxiv.org/abs/math/0507543 | |
| dc.identifier | Ergodic Theory Dynam. Systems 27 (2007) 743-768 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130834 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37D25 (Primary); 37F10; 37F35; 37C40 (Secondary) | |
| dc.title | Markov extensions and lifting measures for complex polynomials | |
| dc.type | text |