Classical Analysis

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2014/11/10

16:00-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre RAMIS (Toulouse)
DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY OF DYNAMICAL SYSTEMS
[ Abstract ]
We will explain how to get obstructions to the integrability of analytic Hamiltonian Systems (in the classical Liouville sense) using Differential Galois Theory (introduced by Emile Picard at the end of XIX-th century). It is the so-called Morales-Ramis theory. Even if this sounds abstract, there exist efficient algorithms allowing to apply the theory and a lot of applications in various domains.

Firstly I will present basics on Hamiltonian Systems and integrability on one side and on Differential Galois Theory on the other side. Then I will state the main theorems. Afterwards I will describe some applications.