Ergodic Theory and Dynamical Systems



On the measurable dynamics of real rational functions


WEIXIAO SHEN a1
a1 Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK (e-mail: wxshen@maths.warwick.ac.uk)

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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.

(Received December 13 2000)
(Revised June 26 2002)