Invariant measures for meromorphic Misiurewicz maps
- 1 November 2008
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 145 (3) , 685-697
Abstract
We study the existence of finite absolutely continuous invariant measures for meromorphic Misiurewicz maps whose Julia set is the whole sphere. In the rational context, these hypotheses imply that such a measure must exist. We show that it is not so for meromorphic maps unless an additional condition on the behavior of the map, which can be stated in terms of its Nevanlinna characteristic, is satisfied.Keywords
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