Wandering orbit portraits

Author:
Jan Kiwi

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

Published electronically:
November 20, 2001

MathSciNet review:
1873015

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Abstract | References | Similar Articles | Additional Information

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 in the Julia set of a polynomial, provided that has an infinite forward orbit.

**[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.

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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

DOI:
https://doi.org/10.1090/S0002-9947-01-02896-3

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