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arXiv:0804.3753 [math.DS]AbstractReferencesReviewsResources

Measures with positive Lyapunov exponent and conformal measures in rational dynamics

Neil Dobbs

Published 2008-04-23, updated 2010-04-13Version 2

Ergodic properties of rational maps are studied, generalising the work of F.\ Ledrappier. A new construction allows for simpler proofs of stronger results. Very general conformal measures are considered. Equivalent conditions are given for an ergodic invariant probability measure with positive Lyapunov exponent to be absolutely continuous with respect to a general conformal measure. If they hold, we can construct an induced expanding Markov map with integrable return time which generates the invariant measure.

Comments: 22 pages, accepted for publication in Trans. AMS, comments welcome
Journal: Trans. Amer. Math. Soc. 364 (2012), 2803-2824
Categories: math.DS
Subjects: 37F10, 37D25, 37D35
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