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Invariant measures for meromorphic Misiurewicz maps
Published online by Cambridge University Press: 01 November 2008
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 3 , November 2008 , pp. 685 - 697
- Copyright
- Copyright © Cambridge Philosophical Society 2008
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