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Combinatorial rigidity for some infinitely renormalizable unicritical polynomials. (English) Zbl 1218.37060
The paper proves that the a priori bounds property, under Lyubich’s secondary limbs condition, implies the combinatorial rigidity conjecture for infinitely renormalizable maps.

MSC:
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
37F25 Renormalization of holomorphic dynamical systems
37F30 Quasiconformal methods and Teichmüller theory, etc. (dynamical systems) (MSC2010)
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