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

 

On the Julia set of König's root-finding algorithms


Author: Gerardo Honorato
Journal: Proc. Amer. Math. Soc. 141 (2013), 3601-3607
MSC (2010): Primary 37F10, 30D05, 37F50; Secondary 65H04
Published electronically: July 1, 2013
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Abstract: As is well known, the Julia set of Newton's method applied to complex polynomials is connected. The family of König's root-finding algorithms is a natural generalization of Newton's method. We show that the Julia set of König's root-finding algorithms of order $ \sigma \geq 3$ applied to complex polynomials is not always connected.


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Additional Information

Gerardo Honorato
Affiliation: Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estr. D. Castorina 110, 22460-320 Rio de Janeiro, Brazil
Email: honorato@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11636-9
PII: S 0002-9939(2013)11636-9
Keywords: Root--finding algorithms, complex dynamics
Received by editor(s): December 12, 2011
Received by editor(s) in revised form: January 5, 2012
Published electronically: July 1, 2013
Additional Notes: The author was supported in part by the Research Network on Low Dimensional Dynamics, PBCT ACT-17-CONICYT, FONDECYT 3120016, Chile and CNPq (The Brazilian National Research Council)
Dedicated: Dedicated to the memory of Sergio Plaza S.
Communicated by: Bryna Kra
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.