Matings of quadratic polynomials. (English) Zbl 0756.58024

Lei, Tan

Ergodic Theory Dyn. Syst. 12, No. 3, 589-620 (1992).

We apply Thurston’s equivalence theory between dynamical systems of postcritically finite branched coverings and rational maps to try to construct, from a pair of polynomials, a rational map. We prove that given two postcritically finite quadratic polynomials \(f_ c: z\mapsto z^ 2+c\) and \(f_{c'}: z\mapsto z^ 2+c'\) one can get a rational map if and only if \(c\), \(c'\) are not in conjugate limbs of the Mandelbrot set.

Reviewer: T.Lei (Lyon)

MSC:

37B99	Topological dynamics
30D05	Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable

Keywords:

holomorphic dynamical system; iteration of polynomials; rational maps

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