On the ergodicity of conformal measures for rational maps with totally disconnected Julia sets

Zhai, Yu

doi:10.1090/S0002-9939-2012-11233-X

On the ergodicity of conformal measures for rational maps with totally disconnected Julia sets
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Proc. Amer. Math. Soc. 140 (2012), 3453-3462 Request permission

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.

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