Hamiltonian systems and Variational equations with polynomial coefficients.
by
Primitivo B. Acosta-Humánez
Universitat Politècnica de Catalunya

The aim of this talk is to show that every autonomous hamiltonian system in which there exists one variational equation with polynomial coefficients has not an additional first integral of rational type, ie the hamiltonian system is not integrable through rationals first integrals. The Morales-Ramis theory, Galois theory in the context of dynamical systems, and the Kovacic algorithm, algorithm to solve second order linear differential equations, are the main tools to prove this statement. This research is a joint work with David Blázquez-Sanz.

Date received: November 2, 2006

Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # catb-20.