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Zbl 1070.37029
Yampolsky, Michael
Complex a priori bounds revisited. (English)
[J] Ann. Fac. Sci. Toulouse, VI. Sér., Math. 12, No. 4, 533-547 (2003). ISSN 0240-2963

The author studies the existence of complex a priori bounds for renormalizations of real quadratic polynomials. He introduces the combinatorial condition of essentially bounded type, which was the subject studied by the author and {\it M. Lyubich} [Ann. Inst. Fourier (Grenoble) 47, 1219--1255 (1997; Zbl 0881.58053)] and gives a new treatment to polynomials satisfying this condition. The approach used in the paper is to consider them as small perturbations of parabolic maps, and to use the rigidity properties of such maps to pass from real a priori bounds to complex ones.
[J.-R. Liang (Shanghai)]

MSC 2000:: *37F25 Renormalization
37E20 Universality, renormalization
37F50 Small divisors, rotation domains and linearization
30D05 Functional equations in the complex domain

Keywords: real quadratic polynomials; complex a priori bounds; parabolic Julia sets; normalizations; perturbations of parabolic maps; rigidity

Citations: Zbl 0881.58053

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