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arXiv · 1607.05057

Semi-classical quantization rules for a periodic orbit of hyperbolic type

Hanen Louati·Michel Rouleux
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Abstract

Determination of periodic orbits for a Hamiltonian system together with their semi-classical quantization has been a long standing problem. We consider here resonances for a $h$-Pseudo-Differential Operator $H(y,hD_y;h)$ induced by a periodic orbit of hyperbolic type at energy $E_0$. We generalize the framework of [G\'eSj], in the sense that we allow for both hyperbolic and elliptic eigenvalues of Poincar\'e map, and show that all resonances in $W=[E_0-\varepsilon_0,E_0+\varepsilon_0]-i]0,h^\delta]$, $0<\delta<1$, are given by a generalized Bohr-Sommerfeld quantization rule.

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Hanen Louati, Michel Rouleux. 2016-07-18. Semi-classical quantization rules for a periodic orbit of hyperbolic type. https://arxiv.org/abs/1607.05057

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