Abstract
We prove that for every polynomial-like holomorphic mapP, ifaεK (filled-in Julia set) and the componentK aofK containinga is either a point ora is accessible along a continuous curve from the complement ofK andK ais eventually periodic, thena is accessible along an external ray. Ifa is a repelling or parabolic periodic point, then the set of arguments of the external rays converging toa is a nonempty closed “rotation set”, finite (ifK ais not a one point) or Cantor minimal containing a pair of arguments of external rays of a critical point in ℂ. In the Appendix we discuss constructions via cutting and glueing, fromP to its external map with a “hedgehog”, and backward.
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Partially supported by the Edmund Landau Center for Research in Mathematical Analysis, sponsored by the Minerva Foundation (Germany).
Supported by the Polish KBN Grants 210469101 “Iteracje i Fraktale” and 210909101 “Uklady Dynamiczne”.
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Levin, G., Przytycki, F. External rays to periodic points. Israel J. Math. 94, 29–57 (1996). https://doi.org/10.1007/BF02762696
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DOI: https://doi.org/10.1007/BF02762696