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ISSN 1088-6850(e) ISSN 0002-9947(p)

Measures with positive Lyapunov exponent and conformal measures in rational dynamics

Author: Neil Dobbs
Journal: Trans. Amer. Math. Soc. 364 (2012), 2803-2824
MSC (2010): Primary 37F10, 37D25, 37D35
Posted: January 25, 2012
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Abstract: 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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