#### Venue

SNS – Centro De Giorgi.

#### Abstract

Parabolic flows form an intermediate category between elliptic and hyperbolic flows. They exhibit some characteristics associated with non-chaotic systems, and some associated with highly chaotic ones. A fundamental example is the horocycle flow on hyperbolic surfaces and, more generally, homogeneous flows generated by multiplication by a unipotent element on a Lie group. It is much more difficult to produce examples of non-homogeneous parabolic flows, since perturbations usually lead to hyperbolic flows.

The simplest perturbation, still in the parabolic realm, is given by time-changes. These have been investigated in detail in the case of the horocycle flow and for nilflows. In this talk, we will give a detailed introduction to the classical theory of horocycles and their time-changes, before presenting our result, joint with Livio Flaminio and Davide Ravotti, on rigidity of time-changes of unipotent flows on finite volume quotients of simple Lie groups, which generalizes Ratner’s classical work on the horocycle flow.

Further information is available on the event page on the Indico platform.