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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


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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Additional Information
  • Jan Kiwi
  • Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile
  • Email:
  • 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:
  • MathSciNet review: 1873015