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Invariant measures for meromorphic Misiurewicz maps

Published online by Cambridge University Press:  01 November 2008

JANINA KOTUS  and
GRZEGORZ ŚWIATEK
JANINA KOTUS
Affiliation:
Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Warsaw 00-661, Poland. e-mail: [email protected]
GRZEGORZ ŚWIATEK
Affiliation:
Department of Mathematics, Penn State University, University Park, PA 16802, U.S.A. e-mail: [email protected]
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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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References

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