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Analytic linearization of circle diffeomorphisms. (English) Zbl 1417.37153
Marmi, Stefano (ed.) et al., Dynamical systems and small divisors. Lectures given at the C. I. M. E. summer school, Cetraro, Italy, June 13–20, 1998. Berlin: Springer. Lect. Notes Math. 1784, 125-173 (2002).
From the text: Rotations on \(\mathbb{T}\) have very simple dynamics. PoincarĂ© asked under which condition a given homeomorphism \(f\) of \(\mathbb{T}\) is equivalent (in some sense, e.g.: measurably, topologically, smoothly, analytically, etc.) to some rotation. He also gave a first answer to this question, today known as Poincare’s classification theorem.
For the entire collection see [Zbl 0989.00040].

37E10 Dynamical systems involving maps of the circle
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
37E20 Universality and renormalization of dynamical systems
37E45 Rotation numbers and vectors
37F25 Renormalization of holomorphic dynamical systems
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics