Wednesday, May 19, 2010

Splitting of invariant manifolds for the Hamiltonian-Hopf bifurcation

José Pedro Gaivão
(University of Warwick)

Abstract: We study homoclinic orbits near a Hamiltonian-Hopf bifurcation. It is well known that in this case the normal form of the Hamiltonian is integrable at all orders. Therefore the difference between the stable and unstable manifolds is exponentially small and the study requires a method capable to detect phenomena beyond all algebraic orders provided by the normal form theory. We establish an asymptotic expansion for a homoclinic invariant which quantitatively describes the transversality of the invariant manifolds. An application of these methods to the Swift-Hohenberg equation is considered.

Wednesday, May 19, 2010
Time: 14h30
Room: Sala IAPMEI, Edificio Quelhas, ISEG