# Jerusalem Mathematics Colloquium

Thursday, 22 April 1999, 4:00 pm

Mathematics Bldg., lecture hall 2

##

Professor Leonid Polterovich

(Tel-Aviv University)

"Symplectic rigidity in Ergodic Theory"

** Abstract: **

It was proved by Liouville that dynamical systems of Classical
Mechanics preserve the volume in the phase space. Later on it was
noticed that in fact there exists a more delicate invariant -- a
differential 2-form called the symplectic structure. The preservation
of volume by mechanical motions has been attracting a lot of attention
for more than a century. It served as the main stimulating force for
the creation of * Ergodic Theory * - a mathematical discipline which
studies various recurrence properties of measure preserving
transformations. However the significance of the role played by the
invariant 2-form has only been noticed relatively recently. An attempt
to understand the difference between mechanical motions and general
volume preserving diffeomorphisms gave rise to the fast developing
field of * Symplectic Topology * which investigates surprising
rigidity phenomena appearing in the theory of symplectic manifolds and
their morphisms.

What are the ergodic consequences of symplectic rigidity?
Do new powerful symplectic methods help us in the understanding of the
ergodic world?
In the talk we discuss some of the first steps in this direction.

Coffee, Cookies, Company at the faculty lounge at 3:30.

List of talks, 1998-99

List of talks, 1997-98