Rigidity of $C^2$ Infinitely Renormalizable Unimodal Maps

Details Rigidity of $C^2$ Infinitely Renormalizable Unimodal Maps Rigidity of $C^2$ Infinitely Renormalizable Unimodal Maps

1999-05-26

arxiv.org/abs/math/9905171v1

Mathematics

Dynamical Systems

16 pages

Scientific paper

10.1007/s002200050749

Given $C^2$ infinitely renormalizable unimodal maps $f$ and $g$ with a
quadratic critical point and the same bounded combinatorial type, we prove that
they are $C^{1+\alpha}$ conjugate along the closure of the corresponding
forward orbits of the critical points, for some $\alpha>0$.

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