Matings of quadratic polynomials. (English) Zbl 0756.58024

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)


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