### 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.