Semiclassical resonances generated by a closed trajectory of hyperbolic type. (English) Zbl 0637.35027

Gérard, C.; Sjöstrand, J.

Commun. Math. Phys. 108, 391-421 (1987).

Authors’ summary: All the resonances in certain rectangular regions of the complex plane of the Schrödinger operator \(-h^ 2\Delta +V\) when \(h\to 0\) (and more general semiclassical operators) are determined under the assumption that the set of trapped points of energy 0 for the classical flow form a closed trajectory and that the corresponding Poincaré map is hyperbolic.

Reviewer: G.Derfel

MSC:

35J10	Schrödinger operator, Schrödinger equation
35S05	Pseudodifferential operators as generalizations of partial differential operators
37-XX	Dynamical systems and ergodic theory

Keywords:

resonances; rectangular regions; complex plane; Schrödinger operator; semiclassical operators; trapped points of energy 0; Poincaré map

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