Semiclassical resonances associated with a periodic orbit

详细

We consider resonances for a h-pseudo-differential operator H(x, hD_x; h) induced by a periodic orbit of hyperbolic type. We generalize the framework of Gérard and Sjöstrand, in the sense that we allow hyperbolic and elliptic eigenvalues of the Poincarémap, and look for so-called semi-excited resonances with imaginary part of magnitude −h log h, or h^δ, with 0 < δ < 1.