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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Wandering orbit portraits

Author: Jan Kiwi
Journal: Trans. Amer. Math. Soc. 354 (2002), 1473-1485
MSC (2000): Primary 37F10, 37F20
Published electronically: November 20, 2001
MathSciNet review: 1873015
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Abstract: We study a counting problem in holomorphic dynamics related to external rays of complex polynomials. We give upper bounds on the number of external rays that land at a point $z$ in the Julia set of a polynomial, provided that $z$has an infinite forward orbit.

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  • [At] P. Atela, Bifurcations of dynamical rays in complex polynomials of degree two, Ergod. Th. & Dynam. Sys. 12 (1992), 401-423. MR 94d:58128
  • [BL] A. Blokh and G. Levin, Growing trees, laminations and the dynamics on the Julia set, Preprint IHES, September 1999.
  • [CG] L. Carleson and T. W. Gamelin, Complex Dynamics, Springer-Verlag, 1993. MR 94h:30033
  • [D] A. Douady.
    Description of compact sets in C.
    In Topological Methods in Modern Mathematics. Publish or Perish, 1993. MR 94g:58185
  • [DH] A. Douady and J. H. Hubbard, Étude dynamique des polynomes complexes I, II, Publ. Math. Orsay, 1984-1985. MR 87f:58072a; MR 87f:58072b
  • [G] L. R. Goldberg, Fixed Points of Polynomial Maps I, Ann. Scient. École Norm. Sup., $ 4^{e}$ série 25 (1992), 679-685. MR 94g:58107
  • [GM] L. R. Goldberg and J. Milnor, Fixed Points of Polynomial Maps II: Fixed Point Portraits, Ann. Scient. École Norm. Sup., $ 4^{e}$ série 26 (1993), 51-98. MR 95d:58107
  • [Ke] K. Keller. Invariant factors, Julia equivalences and the (abstract) Mandelbrot set. Lecture Notes in Mathematics, 1732. Springer-Verlag, Berlin, 2000. CMP 2000:13
  • [Ki1] J. Kiwi, Rational Rays and Critical Portraits of Complex Polynomials, Thesis, SUNY at Stony Brook, 1997. (Stony Brook IMS Preprint 1997/15)
  • [Ki2] J. Kiwi, Rational laminations of complex polynomials, pp 111-154 in Laminations and Foliations in Geometry, Topology and Dynamics, ed. M. Lyubich et al., Contemporary Mathematics 269, 2001. CMP 2001:08
  • [L] G. Levin, On backward stability of holomorphic dynamical systems, Fundamenta Mathematicae 158 (1998), 97-107. MR 99j:58171
  • [M1] J. Milnor, Dynamics in one complex variable: Introductory Lectures, Vieweg, 1999. CMP 2000:03
  • [M2] J. Milnor, Periodic orbits, external rays and the Mandelbrot set: an expository account, pp 277-331 in Géométrie complexe et sytèmes dynamiques (Orsay, 1995), edited by M. Flexor et al., Astérique 261, 2000.
  • [Th] W. P. Thurston, On the combinatorics of iterated rational maps, Manuscript, 1985.

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Additional Information

Jan Kiwi
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

Received by editor(s): April 11, 2000
Received by editor(s) in revised form: March 29, 2001
Published electronically: November 20, 2001
Additional Notes: Supported by “Proyecto Fondecyt #1990436”, “Fundación Andes, Chile” and “Cátedra Presidencial en Geometría”.
Article copyright: © Copyright 2001 American Mathematical Society