Dynamics of renormalization operators

Dynamics of renormalization operators

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Artur Avila, Director of Research, Instituto Nacional de Matem√°tica Pura e Aplicada (IMPA)
Fine Hall 214

It is a remarkable characteristic of some classes of low-dimensional dynamical systems that their long time behavior at a short spatial scale is described by an induced dynamical system in the same class. The renormalization operator that relates the original and the induced transformations can then be iterated. We will discuss how features (such as hyperbolicity) of this "dynamics in parameter space" impact the underlying systems, especially in the case of typical parameters.