an:00086327
Zbl 0756.58024
Lei, Tan
Matings of quadratic polynomials
EN
Ergodic Theory Dyn. Syst. 12, No. 3, 589-620 (1992).
00011018
1992
j
37B99 30D05
holomorphic dynamical system; iteration of polynomials; rational maps
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.
T.Lei (Lyon)