Measures with positive Lyapunov exponent and conformal measures in rational dynamics

Details Measures with positive Lyapunov exponent and conformal measures in rational dynamics Measures with positive Lyapunov exponent and conformal measures in rational dynamics

2008-04-23

arxiv.org/abs/0804.3753v2

Trans. Amer. Math. Soc. 364 (2012), 2803-2824

Mathematics

Dynamical Systems

22 pages, accepted for publication in Trans. AMS, comments welcome

Scientific paper

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.

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