Monday February 3, 2003

Speaker: Raj Prasad (UML)

Title: Typical dynamics for volume preserving homeomorphisms

Abstract: Many physical systems which evolve in time often preserve a natural volume on the state space. After Birkhoff's proof of the ergodic theorem it became important not only to give examples of ergodic transformations, but also to show that (paraphrasing Birkhoff) they were "typical". While they were Junior Fellows at Harvard in the 1930's, J.C. Oxtoby and S.M. Ulam worked on this conjecture of G.D. Birkhoff that ergodicity is the "general case" for volume preserving homeomorphisms of the cube (or a compact manifold).

In this talk I will survey their work and later developments extending the result of Oxtoby and Ulam in different directions. I hope to describe a simple self contained proof of their result from basic principles. No knowledge of ergodic theory will be presumed.