**SMS scnews item created by Daniel Daners at Thu 7 Mar 2013 1212**

Type: Seminar

Distribution: World

Expiry: 18 Mar 2013

**Calendar1: 18 Mar 2013 1400-1500**

**CalLoc1: AGR Carslaw 829**

Auth: daners@como.maths.usyd.edu.au

### PDE Seminar

# Non-existence & existence of integrals that are polynomial in momenta

### Matveev

Vladimir S. Matveev

University of Jena, Germany

18th March 2013 14:00-15:00, Carslaw Room 829 (AGR)

## Abstract

I will consider natural Hamiltonian systems with two degrees of freedom and
speak about the existence and nonexistence of integrals that are polynomial in
momenta.This problem can be reformulates as the existence and construction of
solutions of a certain system of PDE. I will mostly discuss the following questions:
given a metric, how to prove the (non)existence of an integral of a given degree,
and how to find it explicitly? I will explain the classical and modern methods to
study this question. As an application, I will present new systems admitting an
integral of degree 3 in momenta and a solution of a problem explicitly stated by J.
Brink

Check also the PDE
Seminar page. Enquiries to Florica
Cîrstea or Daniel Daners.