Nice sets and invariant densities in complex dynamics
Dynamical Systems
2012-04-02 v3
Abstract
In complex dynamics, we construct a so-called nice set (one for which the first return map is Markov) around any point which is in the Julia set but not in the post-singular set, adapting a construction of Juan Rivera-Letelier. This simplifies the study of absolutely continuous invariant measures. We prove a converse to a recent theorem of Kotus and Swiatek, so for a certain class of meromorphic maps the absolutely continuous invariant measure is finite if and only if an integrability condition is satisfied.
Cite
@article{arxiv.0902.3140,
title = {Nice sets and invariant densities in complex dynamics},
author = {Neil Dobbs},
journal= {arXiv preprint arXiv:0902.3140},
year = {2012}
}
Comments
11 pages, Lemma 10 was, ahem, missing. Other than that, it's just a lot cleaner