Width of resonances created by homoclinic orbits : isotropic fixed point case (Spectral and Scattering Theory and Related Topics)

Abstract

We give a resonance free domain near an energy trapped by homoclinic orbits associated with a hyperbolic xed point. We study the case where the xed point is isotropic and the outgoing manifold and the incoming one intersect tangentially, and show that, under some geometrical assumption, the resonance width is larger than a multiple of h=j/|log h|.