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Conformal Geometry and Dynamics

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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: 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

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.