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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Connectedness of the basin of attraction
for rational maps


Author: Krzysztof Baranski
Journal: Proc. Amer. Math. Soc. 126 (1998), 1857-1866
MSC (1991): Primary 58F23
MathSciNet review: 1443144
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Abstract: We prove some results concerning degree of a rational map on the immediate basin $B(s)$ of an attracting fixed point $s$. In particular, if $B(s)$ contains all but two critical points or values counted with multiplicity, then the entire basin of attraction is connected. For any number $k \geq 3$ we give examples of rational maps with disconnected basin of an attracting fixed point such that there are exactly $k$ critical points outside the immediate basin of attraction.


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Additional Information

Krzysztof Baranski
Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Email: baranski@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04184-7
PII: S 0002-9939(98)04184-7
Received by editor(s): May 1, 1996
Received by editor(s) in revised form: November 14, 1996
Additional Notes: Research supported by Polish KBN Grant No 2 P301 01307.
Communicated by: Mary Rees
Article copyright: © Copyright 1998 American Mathematical Society