Observable events and typical trajectories in finite and infinite dimensional dynamical systems
speaker: Lai-Sang Young (Courant Institute of Mathematical Sciences - New York University)abstract: 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 relevant. I will begin with a discussion of these concepts for general dynamical systems including those with attractors, offering 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 greatly improve the situation. In the second part of my talk I will consider infinite dimensional systems such as semi-flows arising from dissipative evolutionary PDEs, and discuss the extent to which the ideas above can be generalized to infinite dimensions, proposing a notion of "typical solutions" in this context.
timetable:
Fri 22 Apr, 16:00 - 17:00, Aula Dini
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