Abstract: Hamiltonian differential inclusions, with Hamiltonians concave in one variable, convex in the other, arise in optimality conditions for convex control problems. Under strict convexity assumptions, the phase space for the Hamiltonian inclusion resembles that of a linear system with eigenvalues of opposite signs.

The talk will discuss Hamiltonians with a large set of saddle points (the presence of which automatically excludes any strict convexity or concavity). Solutions to corresponding differential inclusions will display some strange behavior; however, a few features of the familiar picture for mentioned linear systems can be recovered.

Time permitting, optimal control applications of our analysis will be mentioned. The talk requires minimal background in analysis and most of the arguments will involve pictures.