Seminari del Dipartimento di Matematica

Seminario del 2011

S. Fujiie (Ritsumeikan University, Kyoto, Giappone)

"The semiclassical width of resonances created by homoclinic trajectories" (joint work with J.-F.Bony, T.Ramond and M.Zerzeri)

fisica matematica

Resonances of the Schroedinger operator near the real axis are closely related with the underlying classical mechanics. Recently, it has been proved that the width (imaginary part) of resonances is greater than a constant multiple of the semiclassical parameter if the trapped set of the classical mechanics is hyperbolic periodic trajectories of Hausdorff dimension less than 2. We will consider the case where the trapped set contains a hyperbolic fixed point, and obtain the same result about the width of resonances even when the dimension of the trapped trajectories is large out of the fixed point. The key of the method is the propagation formula of WKB solutions near a hyperbolic fixed point from the incoming stable manifold to the outgoing one.