On the ergodicity of conformal measures for rational maps with totally disconnected Julia sets
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Abstract:
Let $f$ be a non-hyperbolic rational map with totally disconnected Julia set whose Fatou set is an attracting domain. In this paper, we prove that the number of ergodic components of any conformal measure for $f$ is bounded by the number of critical points in its Julia set.References
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Additional Information
- Yu Zhai
- Affiliation: Department of Mathematics, School of Science, China University of Mining and Technology (Beijing), Beijing 100083, People’s Republic of China
- Email: zhaiyu@amss.ac.cn
- Received by editor(s): October 22, 2010
- Received by editor(s) in revised form: April 6, 2011
- Published electronically: February 16, 2012
- Additional Notes: The author was supported in part by China Postdoctoral Science Foundation Grant #20080440543.
- Communicated by: Bryna Kra
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3453-3462
- MSC (2010): Primary 37F10, 37F20; Secondary 28D99
- DOI: https://doi.org/10.1090/S0002-9939-2012-11233-X
- MathSciNet review: 2929014