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Nice sets and invariant densities in complex dynamics

Published online by Cambridge University Press:  22 June 2010

NEIL DOBBS
NEIL DOBBS*
Affiliation:
Institutionen for Matematik, KTH, Lindstedtsvagen 25, 100 44 Stockholm, Sweden e-mail: neil.dobbs@gmail.com
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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 Rivera–Letelier. This simplifies the study of absolutely continuous invariant measures. We prove a converse to a recent theorem of Kotus and Świątek, so for a certain class of meromorphic maps the absolutely continuous invariant measure is finite if and only if an integrability condition is satisfied.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 1 , January 2011 , pp. 157 - 165
Copyright
Copyright © Cambridge Philosophical Society 2010

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