Lai-Sang Young (NYU Courant) (Videoconference)
TITLE :
Observable events and typical trajectories in finite and infinite听dimensional dynamical systems
ABSTRACT :
The terms "observable events" and "typical trajectories" in the title听should really be between quotation marks, because what is typical and/or听observable is a matter of interpretation. For dynamical systems on听finite dimensional spaces, one often equates observable events with听positive Lebesgue measure sets, and invariant distributions that reflect听the large-time behaviors of positive Lebesgue measure sets of initial听conditions (such as Liouville measure for Hamiltonian systems) are听considered to be especially important. I will begin by introducing
these concepts for general dynamical systems -- including those with听attractors -- describing a simple dynamical picture that one might hope听to be true. This picture does not always hold, unfortunately, but a听small amount of random noise will bring it about. In the second part of听my talk I will consider infinite dimensional systems such as semi-flows听arising from dissipative evolutionary PDEs. I will discuss the extent听to which the ideas above can be generalized to infinite dimensions, and听propose a notion of ``typical solutions".
PLACE :
Zoom meeting id:
ID de r茅union : 170 851 981
Mot de passe : 942210
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