Dynamical Systems Seminar

Deformations of one-dimensional dynamical systems

by Prof. Daniel Smania (ICMC - USP)



Sala Conferenze - Centro De Giorgi

Perhaps one of the main features of one-dimensional dynamics (either real or complex) is that the theory of deformations is rich. By this we mean that the topological classes of such maps often are infinite dimensional manifolds, but with finite codimension. They  are kind of "almost"  structurally stable! Moreover for smooth families of maps inside a given topological class the associated family of conjugacies also moves in a smooth way.  There are various applications in the study of renormalisation theory and linear response theory. There is a nice theory  in complex dynamics but for  real maps with finite smoothness on the interval our current understanding is far behind the complex setting. We will discuss recent developments obtained in joint work with  Clodoaldo Ragazzo but also some results with  Viviane Baladi and Amanda de Lima. Ergodic theory will be a crucial tool.