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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
DOI: https://doi.org/10.1090/S0002-9947-2012-05366-9
Published electronically: January 25, 2012
MathSciNet review: 2888229
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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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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

DOI: https://doi.org/10.1090/S0002-9947-2012-05366-9
Received by editor(s): April 23, 2008
Received by editor(s) in revised form: January 20, 2010
Published electronically: January 25, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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