On a theorem of Fatou

  • Ricardo Mañé
Article

DOI: 10.1007/BF01231694

Cite this article as:
Mañé, R. Bol. Soc. Bras. Mat (1993) 24: 1. doi:10.1007/BF01231694

Abstract

We prove a result on the backward dynamics of a rational function nearby a point not contained in the ω-limit set of a recurrent critical point. As a corollary we show that a compact invariant subset of the Julia set, not containing critical or parabolic points, and not intersecting the ω-limit set ofrecurrent critical points, is expanding, thus extending a classical criteria of Fatou. We also prove that the boundary of a Siegel disk is always contained in the ω-limit set of arecurrent critical point.

Copyright information

© Sociedade Brasileira de Matemática 1993

Authors and Affiliations

  • Ricardo Mañé
    • 1
  1. 1.Instituto de Matemática Pura e Aplicada, IMPARio de JaneiroBrasil

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