, Volume 208, Issue 1, pp 91-105

Rigidity of C 2 Infinitely Renormalizable Unimodal Maps

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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.

Received: 16 March 1999 / Accepted: 21 May 1999