Title: Toda maps, cocycles, and canonical systems,
Abstract: I present a discussion of the hierarchy of Toda flows that gives center stage
to the associated cocycles and the maps they induce on the $m$ functions. In
the second part, these ideas are then applied to canonical systems; an
important feature of this discussion will be my proposal that the role of the
shift on Jacobi matrices should now be taken over by the more general class of
twisted shifts.