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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Wandering orbit portraits
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by Jan Kiwi PDF
Trans. Amer. Math. Soc. 354 (2002), 1473-1485 Request permission

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.
References
  • Pau Atela, Bifurcations of dynamic rays in complex polynomials of degree two, Ergodic Theory Dynam. Systems 12 (1992), no. 3, 401–423. MR 1182654, DOI 10.1017/S0143385700006854
  • A. Blokh and G. Levin, Growing trees, laminations and the dynamics on the Julia set, Preprint IHES, September 1999.
  • Lennart Carleson and Theodore W. Gamelin, Complex dynamics, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. MR 1230383, DOI 10.1007/978-1-4612-4364-9
  • Adrien Douady, Descriptions of compact sets in $\textbf {C}$, Topological methods in modern mathematics (Stony Brook, NY, 1991) Publish or Perish, Houston, TX, 1993, pp. 429–465. MR 1215973
  • Radu Bǎdescu, On a problem of Goursat, Gaz. Mat. 44 (1939), 571–577. MR 0000087
  • De Hai Zhang, $q$-deformed Gel′fand-Dikiĭ potentials of quantum deformation KdV equation, Proceedings of the 1992 Nonlinear Science Symposium (Chinese) (Hefei, 1992), 1993, pp. 97–101 (English, with English and Chinese summaries). MR 1228289
  • Lisa R. Goldberg and John Milnor, Fixed points of polynomial maps. II. Fixed point portraits, Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 1, 51–98. MR 1209913, DOI 10.24033/asens.1667
  • K. Keller. Invariant factors, Julia equivalences and the (abstract) Mandelbrot set. Lecture Notes in Mathematics, 1732. Springer-Verlag, Berlin, 2000.
  • J. Kiwi, Rational Rays and Critical Portraits of Complex Polynomials, Thesis, SUNY at Stony Brook, 1997. (Stony Brook IMS Preprint 1997/15)
  • 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.
  • G. Levin, On backward stability of holomorphic dynamical systems, Fund. Math. 158 (1998), no. 2, 97–107. MR 1656942, DOI 10.4064/fm-158-2-97-107
  • J. Milnor, Dynamics in one complex variable: Introductory Lectures, Vieweg, 1999.
  • 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.
  • 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
  • Email: jkiwi@mat.puc.cl
  • 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”.
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 1473-1485
  • MSC (2000): Primary 37F10, 37F20
  • DOI: https://doi.org/10.1090/S0002-9947-01-02896-3
  • MathSciNet review: 1873015