Semi-classical resonances associated with a periodic orbit of hyperbolic type

2016/06/20 by Louati, Hanen, Rouleux, Michel
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1606.06180

Abstract

We consider in this Note resonances for a h-Pseudo-Differential Operator H(x,hD_x;h) on L²(M) induced by a periodic orbit of hyperbolic type, as arises for Schrödinger operator with AC Stark effect when M=\bf Rⁿ, or the geodesic flow on an axially symmetric manifold M, extending Poincaré example of Lagrangian systems with 2 degrees of freedom. We generalize the framework of [GéSj], in the sense that we allow for hyperbolic and elliptic eigenvalues of Poincaré map, and look for so-called semi-excited resonances with imaginary part of magnitude -hlog h, or h^s, with 0

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