Available in electronic format
Available in print format		 Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Wandering orbit portraits

Author(s): Jan Kiwi
Journal: Trans. Amer. Math. Soc. 354 (2002), 1473-1485.
MSC (2000): Primary 37F10, 37F20
Posted: November 20, 2001
Retrieve article in: PDF DVI PostScript
This article is available free of charge

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

References:

[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.

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 37F10, 37F20

Retrieve articles in all Journals with MSC (2000): 37F10, 37F20

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: 10.1090/S0002-9947-01-02896-3
PII: S 0002-9947(01)02896-3
Received by editor(s): April 11, 2000
Received by editor(s) in revised form: March 29, 2001
Posted: November 20, 2001
Additional Notes: Supported by ``Proyecto Fondecyt \#1990436'', ``Fundación Andes, Chile'' and ``Cátedra Presidencial en Geometría''.
Copyright of article: Copyright 2001, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google