Markov extensions and lifting measures for complex polynomials
Dynamical Systems
2007-06-13 v2
Abstract
For polynomials 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 -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 -conformal measure is liftable if and only if the set of points with positive Lyapunov exponent has positive measure.
Cite
@article{arxiv.math/0507543,
title = {Markov extensions and lifting measures for complex polynomials},
author = {Henk Bruin and Mike Todd},
journal= {arXiv preprint arXiv:math/0507543},
year = {2007}
}
Comments
Some changes have been made, in particular to Sections 2 and 3, to clarify the exposition. Typos have been corrected and references updated