Title: Rigidity and Renormalization in One Dimensional Dynamical Systems

If two smooth unimodal maps or real analytic critical circle maps have the same bounded combinatorial type then there exists a $C^{1+\alpha}$ diffeomorphism conjugating the two maps along the corresponding critical orbits for some $\alpha>0$. The proof is based on a detailed understanding of the orbit structure of an infinite dimensional dynamical system: the renormalization operator.

1991 Mathematics Subject Classification:

Keywords and Phrases:

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