Topology and Dynamics of Integrable Systems
Leo Butler (University of Edinburgh)
Tuesday 8th April, 2008 15:00-16:00 Mathematics Building, room 516
Integrable systems are widely encountered in many branches of mathematics. For the purposes of this talk, an integrable system is a dynamical system whose phase space is foliated by invariant tori and on each invariant torus the system is a linear flow. Of course this picture is deceptively simple since the foliation by tori is singular. Two natural, complementary questions arise: are the dynamics of an integrable system on its singular set constrained? and, are there global topological restrictions on the phase space of an integrable system? This talk will discuss recent results concerning these questions. Time permitting, we will see how these questions relate to the geometrization conjecture, exotic spheres, and Anosov diffeomorphisms.