On quasi-invariant curves

Ricardo Pérez-Marco (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

Quasi-invariant curves are used in the study of hedgehog dynamics. Denjoy-Yoccoz lemma is the preliminary step for Yoccoz's complex renormalization techniques for the study of linearization of analytic circle diffeomorphisms. We give a geometric interpretation of Denjoy-Yoccoz lemma using the hyperbolic metric that gives a direct construction of quasi-invariant curves without renormalization.

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Ricardo Pérez-Marco. On quasi-invariant curves. Asterisque, 2020. ⟨hal-01710692v2⟩