Bounds, quadratic differentials and renormalization conjectures

Sullivan, Dennis



Abstract : In the context of smooth folding mappings we verifie certain conjecture by showing bounded return time renormalization is topologically hyperbolic and find the stable and unstable manifolds. The main consequence is the asymptotic geometric rigidity of the Cantor sets defined by the critical orbits. We use the bounds and quadratic differentials on Riemann surface lamination to prove exponential renormalization contraction in a space of holomorphic dynamical systems that contains the limit set of renormalization.




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SULLIVAN, “Bounds, quadratic differentials and renormalization conjectures,” Archives de l'IHES, consulté le 20 mai 2024,