Global Hyperbolicity of Renormalization for C^r Unimodal Maps
Alberto A. Pinto | de Faria , Edson | de Melo, Welington
renormalization | hyperbolicity
In this paper we extend M. Lyubich?s recent results on the global hyperbolicity of renormalization of quadratic-like germs to the space of $C^r$ unimodal maps with quadratic critical points. We show that in this space the bounded-type limit set of the renormalization operator have an invariant hyperbolic structure provided $r>2+\alpha$ with $\alpha $ close to one.