Department of Mathematics, Emory University
Atlanta, GA, 30322, USA
http://www.mathcs.emory.edu/~rudolf
e-mail: rudolf@mathcs.emory.edu

The Lie Group of Fourier Integral Operators and Applications to Hydrodynamics

Abstract:
We endow the group of invertible Fourier integral operators on an open manifold with the structure of an infinite dimensional Lie group. This is done by establishing such structures for the groups of invertible pseudodifferential operators and contact diffeomorphisms on an open manifold with bounded geometry, and gluing these together via a local section of a corresponding exact sequence. We use these Lie group structures to describe Euler's equations as a geodesic flow and the KdV equation as an infinite dimensional Hamiltonian system.