Infinitesimal contraction of the Feigenbaum renormalization operator in the horizontal direction

Details Infinitesimal contraction of the Feigenbaum renormalization operator in the horizontal direction Infinitesimal contraction of the Feigenbaum renormalization operator in the horizontal direction

2002-05-18

arxiv.org/abs/math/0205204v1

Mathematics

Dynamical Systems

5 pages

Scientific paper

In this short note, we give a sketch of a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the Feigenbaum fixed point. The proof uses the non existence of invariant line fields in the Feigenbaum tower (C. McMullen), the topological convergence (D. Sullivan), and a new infinitesimal argument, different from previous methods by C. McMullen and M. Lyubich. The method is very general: for instance, it can be used in the classical renormalization operator and in the Fibonacci renormalization operator.

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