Quebec Mathematical Sciences Colloquium

April 17, 2020 from 16:00 to 17:00 (Montreal/Miami time) Zoom meeting

Observable events and typical trajectories in finite and infinite dimensional dynamical systems

Colloquium presented by Lai-Sang Young (New York University Courant)

The terms "observable events" and "typical trajectories" in the title should really be between quotation marks, because what is typical and/or observable is a matter of interpretation. For dynamical systems on finite dimensional spaces, one often equates observable events with positive Lebesgue measure sets, and invariant distributions that reflect the large-time behaviors of positive Lebesgue measure sets of initial conditions (such as Liouville measure for Hamiltonian systems) are considered to be especially important. I will begin by introducing these concepts for general dynamical systems -- including those with attractors -- describing a simple dynamical picture that one might hope to be true. This picture does not always hold, unfortunately, but a small amount of random noise will bring it about. In the second part of my talk I will consider infinite dimensional systems such as semi-flows arising from dissipative evolutionary PDEs. I will discuss the extent to which the ideas above can be generalized to infinite dimensions, and propose a notion of "typical solutions".