Conformal Geometry and Dynamics

ISSN 1088-4173

 

 

On the dynamics of the McMullen family $ R(z)=z^m +\lambda/z^{\ell}$


Author: Norbert Steinmetz
Journal: Conform. Geom. Dyn. 10 (2006), 159-183
MSC (2000): Primary 37F10, 37F15, 37F45
Published electronically: August 22, 2006
MathSciNet review: 2261046
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we discuss the parameter plane and the dynamics of the rational family $ R(z)=z^m+\lambda/z^{\ell}$, with $ m\ge 2$, $ \ell\ge 1$, and $ 0<\vert\lambda\vert<\infty$.


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Additional Information

Norbert Steinmetz
Affiliation: Fachbereich Mathematik, Universität Dortmund, D-44221 Dortmund, Germany
Email: stein@math.uni-dortmund.de

DOI: http://dx.doi.org/10.1090/S1088-4173-06-00149-4
Keywords: Julia set, Fatou set, quasi-conjugation, polynomial-like mapping, quasi-conformal mapping, Mandelbrot set, parameter plane
Received by editor(s): January 31, 2006
Published electronically: August 22, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.