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Rigidity of $C^2$ Infinitely Renormalizable Unimodal Maps

Wellington de Melo·Alberto Pinto
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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 $C^{1+α}$ conjugate along the closure of the corresponding forward orbits of the critical points, for some $α>0$.

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Wellington de Melo, Alberto Pinto. 1999-05-26. Rigidity of $C^2$ Infinitely Renormalizable Unimodal Maps. https://doi.org/10.1007/s002200050749

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