On the Julia set of König’s root–finding algorithms
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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.References
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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
- 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)
- Communicated by: Bryna Kra
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3601-3607
- MSC (2010): Primary 37F10, 30D05, 37F50; Secondary 65H04
- DOI: https://doi.org/10.1090/S0002-9939-2013-11636-9
- MathSciNet review: 3080182
Dedicated: Dedicated to the memory of Sergio Plaza S.