Institute for Mathematical Sciences

Preprint ims99-6

W. de Melo and A. A. Pinto
Rigidity of C^2 Infinitely Renormalizable Unimodal Maps

Abstract: 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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