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Comparing measures and invariant line fields

Published online by Cambridge University Press:  07 May 2002

VOLKER MAYER
VOLKER MAYER
Affiliation:
UFR de Mathématiques, Université de Lille I, UMR 8524 du CNRS, 59655 Villeneuve d'Ascq Cedex, France (e-mail: [email protected])
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Abstract

We give elementary proofs of two rigidity results. The first one asserts that the maximal entropy measure \mu_f of a rational map f is singular with respect to any given conformal measure excepted if f is a power, Tchebychev or Lattès map. This is a variation of a result of Zdunik. Our second result is an improvement of a theorem of Fisher and Urbański. It gives a sharp description of the exceptional functions that admit invariant line fields which are defined with respect to certain invariant measures

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 2 , April 2002 , pp. 555 - 570
Copyright
2002 Cambridge University Press

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