Rigidity and renormalization in one dimensional dynamical systems
This article reviews the recent development in the renormalization theory of unimodal maps and critical circle maps. 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 orbit for some \(\alpha>0\). The article gives an overview of the proof which is based on a detailed understanding of the orbit structure of infinite-dimensional dynamical systems: the renormalization operator.
scientific article; zbMATH DE number 1184286