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Semiclassical resonances associated with a periodic orbit

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Abstract

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.

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Authors and Affiliations

  1. University of Aix-Marseille, University of Toulon, CNRS, CPT, Paris, France

    H. Louati & M. Rouleux

  2. University of Tunis, El–Manar, Tunis, Tunisia

    H. Louati

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  1. H. Louati
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  2. M. Rouleux
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Correspondence to H. Louati.

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Louati, H., Rouleux, M. Semiclassical resonances associated with a periodic orbit. Math Notes 100, 724–730 (2016). https://doi.org/10.1134/S0001434616110092

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