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On a theorem of Fatou

  • Ricardo Mañé
Article

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.

Keywords

Rational Function Invariant Subset Classical Criterion Parabolic Point Siegel Disk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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