Date(s) : 01/04/2016 - 09/04/2016 iCal
0 h 00 min
The conference will focus on renormalization schemes, which often enable to understand the dynamics of a parabolic or elliptic system in a given family through the study of an auxiliary hyperbolic system. Well-known examples of renormalization include the classical Gauss map, which renormalizes rotations of the circle, the geodesic flow on a surface of constant negative curvature, which renormalizes the corresponding horocycle flow, and more generally the Teichmueller flow and the Rauzy-Veech induction, which provide an effective renormalization scheme for interval exchange transformations.
The core will be the interplay between dynamical systems and arithmetic, and in particular the study of discrete arithmetic algorithms of significance in dynamics and geometry.
We will discuss in particular recent developments in the ergodic theory of continued fractions and their various one and multidimensional generalizations.
Significant importance will be given to fractals arising naturally as geometric pictures of numeration systems and their topological properties, as well as to the application of renormalization techniques in symbolic dynamics.
Centro di Ricerca Matematica Ennio De Giorgi
Collegio Puteano, Scuola Normale Superiore
Piazza dei Cavalieri, 3