EVENT DETAILS AND ABSTRACT

Title: Integrable Hamiltonian Systems with Positive Lebesgue Metric Entropy
Speaker: Leo Butler
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

A completely integrable flow is a flow whose phase space contains an open dense set fibred by invariant tori, and the flow on these tori is a translation-type flow. In the real-analytic category, there are many known obstructions to the integrability of a hamiltonian system. One is this: if $\phi_t$ is real-analytically integrable, then the metric entropy of $\phi_t$ with respect to any smooth measure is zero.

We construct explicit examples of a smoothly integrable hamiltonian flow $\phi_t$ on a Poisson manifold that preserves a canonical smooth measure $m$, and $h_m(\phi_t) > 0$.

The construction yields several additional results, which will also be briefly described.