Renormalization of Unicritical Diffeomorphisms of the Disk

Explore a seminar on the renormalization of unicritical diffeomorphisms of the disk presented by Enrique Pujals from CUNY. Delve into the joint work with S. Crovisier and C. Tresser, which proves that Henon maps with Jacobian smaller than 1/4 on the boundary of zero entropy diffeomorphisms are infinitely renormalizable. Discover the generalization of infinitely renormalizable unimodal maps to dissipative diffeomorphisms of the disk, a concept developed in collaboration with Crovisier, Lyubich, and J. Yang. Learn how these maps converge super-exponentially to one-dimensional unimodal maps under renormalization. Gain insights into the quantitative reformulation of Pesin theory and a novel approach to analyzing 'critical orbits' in higher dimensional settings. This 1 hour 39 minute seminar, conducted in Portuguese, is part of the Dynamic Systems and Ergodic Theory series at the Instituto de Matemática Pura e Aplicada.