Renormalisation structures in complex dynamics

Jeudi 22 février 2018 14:00-15:00 - Davoud Cheraghi - Imperial College London

Résumé : In early 1980’s Douady and Hubbard discovered and used a notion of renormalisation to explain the appearance of homeomorphic copies of the Mandelbrot set inside the Mandelbrot set. Renormalisation structures occur when some large iterate of a quadratic polynomial on some small scale on the complex plane behaves like a quadratic polynomial, which may have a behaviour independent of the original map. Renormalisation structures appear in many forms and are a major obstruction to explaining the dynamics of the map. Such structures with tame geometries have been successfully studied in the last forty years, while other forms of such structures with degenerating geometries remained unexplained until recently. In this talk we discuss these notions of renormalisations, and present recent results concerning renormalisations with degenerating geometries.

Lieu : Institut de Mathématique d'Orsay, salle 2L8

Notes de dernières minutes : Café culturel à 13h par Jacek Graczyk.

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