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On the measurable dynamics of real rational functions

By Weixiao Shen

Abstract

Let f be a real rational function with all critical points on the extended real axis and of even order. Then:\ud \ud (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\ud \ud (2) f|J(f) has only finitely many ergodic components

Topics: QA
Publisher: Cambridge University Press
Year: 2003
OAI identifier: oai:wrap.warwick.ac.uk:763

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