This talk will focus on locally Hamiltonian flows on surfaces, namely smooth two-dimensional flows which are local solutions of Hamiltonian differential equations. We will present a survey of results concerning the chaotic properties, in particular mixing properties, of this class of flows. We will then discuss the deviation phenomena exhibited by ergodic integrals of smooth functions. Recent results on this phenomenon and applications to ergodicity of extensions are based on joint works with K. Fraczek and with P. Berk and F. Trujillo.
Friday, November 3, 9:00