Ergodic Theory and Dynamical Systems

On the measurable dynamics of real rational functions

a1 Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK (e-mail:

Article author query
shen w   [Google Scholar] 


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)