External rays to periodic points

G. Levin*, F. Przytycki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We prove that for every polynomial-like holomorphic map P, if a ∈ K (filled-in Julia set) and the component Ka of K containing a is either a point or a is accessible along a continuous curve from the complement of K and Ka is eventually periodic, then a is accessible along an external ray. If a is a repelling or parabolic periodic point, then the set of arguments of the external rays converging to a is a nonempty closed "rotation set", finite (if Ka is not a one point) or Cantor minimal containing a pair of arguments of external rays of a critical point in ℂ\K. In the Appendix we discuss constructions via cutting and glueing, from P to its external map with a "hedgehog", and backward.

Original languageAmerican English
Pages (from-to)29-57
Number of pages29
JournalIsrael Journal of Mathematics
Volume94
DOIs
StatePublished - 1996

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