Ergodic Theory and Dynamical Systems

Research Article

Matings of quadratic polynomials

Tan Leia1

a1 Laboratoire de Mathématiques, Ecole Normale Supérieure de Lyon, 46 allée d'ltalie, 69364Lyon cedex 07, France

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: zz2+c and fc:zz2+c′, one can get a rational map if and only if c, c′ are not in conjugate limbs of the Mandelbrot set.

(Received September 16 1991)