Abstract and Applied Analysis
Volume 2013 (2013), Article ID 536910, 10 pages
http://dx.doi.org/10.1155/2013/536910
Research Article

Bulbs of Period Two in the Family of Chebyshev-Halley Iterative Methods on Quadratic Polynomials

Alicia Cordero,1,2 Juan R. Torregrosa,1,2 and Pura Vindel1,2

1Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Cno. de Vera s/n, 46022 Valencia, Spain
2Instituto de Matemáticas y Aplicaciones de Castellón, Universitat Jaume I, Avenida de Vicent Sos Baynat s/n, 12071 Castelló de la Plana, Spain

Received 1 March 2013; Accepted 18 April 2013

Academic Editor: Jan Andres

Copyright © 2013 Alicia Cordero et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The parameter space associated to the parametric family of Chebyshev-Halley on quadratic polynomials shows a dynamical richness worthy of study. This analysis has been initiated by the authors in previous works. Every value of the parameter belonging to the same connected component of the parameter space gives rise to similar dynamical behavior. In this paper, we focus on the search of regions in the parameter space that gives rise to the appearance of attractive orbits of period two.