## Abstract

We prove that for every polynomial-like holomorphic map P, if a ∈ K (filled-in Julia set) and the component K_{a} of K containing a is either a point or a is accessible along a continuous curve from the complement of K and K_{a} 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 K_{a} 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 language | English |
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Pages (from-to) | 29-57 |

Number of pages | 29 |

Journal | Israel Journal of Mathematics |

Volume | 94 |

DOIs | |

State | Published - 1996 |