Functional Analysis and Applications Seminar 

24/11/2006, 14:00 — 15:00 — Room P3.10, Mathematics Building
António Ferreira dos Santos, Instituto Superior Técnico, U.T. Lisboa

Lax equations, factorization and Riemann-Hilbert problems

In this talk the problem of existence and calculation of solutions to Lax equations that define finite-dimensional integrable systems is studied. The method presented is based on Wiener-Hopf factorization and related Riemann-Hilbert problems on Riemann surfaces. The idea behind the method was first proposed by Semenov-Tian-Shansky but has never been applied in a situation where a nontrivial function factorization is required. An example of a dynamical system associated with an elliptic curve is given.