Measures with positive Lyapunov exponent and conformal measures in rational dynamics
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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.References
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Additional Information
- Neil Dobbs
- Affiliation: Department of Mathematics, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden
- Address at time of publication: IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598
- Email: neil.dobbs@gmail.com
- Received by editor(s): April 23, 2008
- Received by editor(s) in revised form: January 20, 2010
- Published electronically: January 25, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 2803-2824
- MSC (2010): Primary 37F10, 37D25, 37D35
- DOI: https://doi.org/10.1090/S0002-9947-2012-05366-9
- MathSciNet review: 2888229