**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.

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