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Matings of quadratic polynomials

Published online by Cambridge University Press:  19 September 2008

Tan Lei
Tan Lei
Affiliation:
Laboratoire de Mathématiques, Ecole Normale Supérieure de Lyon, 46 allée d'ltalie, 69364Lyon cedex 07, France
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Abstract

We apply Thurston's equivalence theory between dynamical systems of post-critically finite branched coverings and rational maps, to try to construct, from a pair of polynomials, a rational map. We prove that given two post-critically finite quadratic polynomials fc: z→z2+c and fc:z→ z2+c′, one can get a rational map if and only if c, c′ are not in conjugate limbs of the Mandelbrot set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 3 , September 1992 , pp. 589 - 620
Copyright
Copyright © Cambridge University Press 1992

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