Single orbits and Wiener-Wintner theorem

RESUMEN      A single-orbit approach to dynamics links the global properties of a dynamical system with the behaviour of its orbits. During the talk, I shall discuss what can be deduced about the system from the existence of an orbit satisfying the conclusion of the Wiener-Wintner theorem (a Wiener-Wintner generic orbit). I will examine the spectrum of ergodic measures by examining the behaviour of their Wiener–Wintner generic points. Moreover, by investigating the properties of a “regular” subclass of such points, I shall characterise ergodic measures with discrete spectrum.

In joint work with Melih Emin Can, Dominik Kwietniak, and Piotr Oprocha, we introduce a metric rho-bar on the space of invariant measures that induces a topology stronger than the weak-* topology.

Additionally, I will also show that for any fixed characteristic class on a topological dynamical system, the set of ergodic measures belonging to that class is closed with respect to the topology induced by rho-bar.

Posted on Nov 21, 2025 in Dynamical Systems, Seminars