Institut für Mathematik


Modul:   MAT760  Ergodic theory and dynamical systems seminar

Deformations of one-dimensional dynamical systems

Vortrag von Prof. Dr. Daniel Smania

Datum: 30.05.23  Zeit: 13.30 - 14.30  Raum: ETH HG G 43

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.