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On the measurable dynamics of real rational functions

Published online by Cambridge University Press:  20 June 2003

WEIXIAO SHEN
WEIXIAO SHEN
Affiliation:
Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK (e-mail: [email protected])
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Abstract

Let f be a real rational function with all critical points on the extended real axis and of even order. Then:

(1) f carries no invariant line field on the Julia set unless it is doubly covered by an integral torus endomorphism (a Lattés example); and

(2) f|J(f) has only finitely many ergodic components.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 3 , June 2003 , pp. 957 - 983
Copyright
2003 Cambridge University Press

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