Spectral monodromy in classical completely integrable or quasi-integrable cases

Quang Sang Phan (1)

1 UJ - Uniwersytet Jagielloński w Krakowie = Jagiellonian University

The spectral monodromy is a combinatorial invariant, defined directly from the spectrum of certain non-selfadjoint classical operators. It is a obstruction against the global lattice structure of the spectrum, seen as a discrete subset of points in the complex plane, and in the semi-classical limit. We work with small non-selfadjoint perturbations of classical selfadjoint operators with two degrees of freedom, assuming that the (semi-)classical principal symbol of the unperturbed part is in two different cases: completely integrable system in the first case, and quasi-integrable one with a globally (non-degenerate) isoenergetic condition in the second case. In each case, the spectral monodromy allows to recover the corresponding classical monodromy.

Mots clés: asymptotic spectral; Hamiltonian systems; non-selfadjoint; spectral analysis; KAM theory; asymptotic spectral.

Domaines: Physique mathématique [math-ph]

Quang Sang Phan. Spectral monodromy in classical completely integrable or quasi-integrable cases. 2014. ⟨hal-00991687v2⟩