## View abstract

### Invited talk

Thursday, July 22, 14:45 ~ 15:45 UTC-3

## Observable events and typical trajectories in dynamical systems

### Lai-Sang Young

#### New York University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak7ed8709785afc1fdae88003ddd92c08d').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy7ed8709785afc1fdae88003ddd92c08d = 'lsy' + '&#64;'; addy7ed8709785afc1fdae88003ddd92c08d = addy7ed8709785afc1fdae88003ddd92c08d + 'c&#105;ms' + '&#46;' + 'ny&#117;' + '&#46;' + '&#101;d&#117;'; var addy_text7ed8709785afc1fdae88003ddd92c08d = 'lsy' + '&#64;' + 'c&#105;ms' + '&#46;' + 'ny&#117;' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak7ed8709785afc1fdae88003ddd92c08d').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy7ed8709785afc1fdae88003ddd92c08d + '\'>'+addy_text7ed8709785afc1fdae88003ddd92c08d+'<\/a>';

I will present ideas related to typical solutions" for finite and infinite dimensional dynamical systems, deterministic or stochastic. In finite dimensions, one often equates observable events with positive Lebesgue measure sets, and view invariant measures that reflect large-time behaviors of positive Lebesgue measure sets of initial conditions as physically relevant. Accepting these ideas, there is a simple and very nice picture that one might hope to be true. Reality is messier, unfortunately, at least for deterministic systems. I will argue that the addition of a small amount of random noise will bring this picture about. As for infinite dimensional systems, such as those defined by semi-flows generated by evolutionary PDEs, a different notion of observability is needed. I will finish with some results that suggest a notion of "typical solutions" for certain kinds of infinite dimensional systems.

Joint work with Alex Blumenthal (Georgia Institute of Technology) and others.