Deformations of one-dimensional dynamical systems
Daniel Smania (ICMC-USP)

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 on the interval our current understanding is far behind the complex setting. We will discuss the recents developments obtained in joint work with several collaborators: Viviane Baladi, Amanda de Lima and more recently Clodoaldo Ragazzo. Ergodic theory will be a crucial tool.