On a theorem of Fatou
- Cite this article as:
- Mañé, R. Bol. Soc. Bras. Mat (1993) 24: 1. doi:10.1007/BF01231694
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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.