invites you to a


to be presented by

Professor Paul H Rabinowitz

University of Wisconsin–Madison

Member of the National Academy of Sciences

The lectures will be held in

Room 232
Amado Mathematics Building

Technion - Israel Institute of Technology
Haifa, Israel

Lecture I:  Monday 19 December, 2005 at 15:30


Towards an Aubry-Mather Theory for PDE's I

(a) The work of Moser and then of Bangert towards a PDE version of the Aubry-Mather theory of invariant curves for self maps of an annulus


(b) The recent developments due to Rabinowitz and Stredulinsky which introduce renormalized functionals to the Moser-Bangert setting and use them to obtain a large variety of solutions of the PDE's.

Lecture II:  Wednesday, 21 December, 2005  at 15:30


Towards an Aubry-Mather Theory for PDE's II


This lecture will both discuss some results not given in the first lecture and sketch the proofs of some of the surveyed results.

Lecture III:  Thursday, 22 December, 2005  at 15:30


Homoclinic Solutions of Hamiltonian Systems with
Double Well Potentials


A survey will be given of existence results for heteroclinic and homoclinic solutions of the Hamiltonian system

q" + V_q(t,q) =0

where q is in R^n and V is either a periodic or double well potential in q. Some recent work on a case in which the bottoms of the wells are are different levels will be discussed in more detail.


Due to construction in the Amado Mathematics Building the venue of the lectures might change. In the event of such a change an announcement will be posted on-line. We advise that you check with the dept. before attending the lectures at: 04-829-4272 ,04-829-4278