  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.
