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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Connectedness of the basin of attraction for rational maps
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by Krzysztof Barański PDF
Proc. Amer. Math. Soc. 126 (1998), 1857-1866 Request permission

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 Barański
  • Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
  • MR Author ID: 366411
  • Email: baranski@mimuw.edu.pl
  • 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
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 1857-1866
  • MSC (1991): Primary 58F23
  • DOI: https://doi.org/10.1090/S0002-9939-98-04184-7
  • MathSciNet review: 1443144