03-135 COLIN de VERDIERE Yves

THE LEVEL CROSSING PROBLEM IN SEMI-CLASSICAL ANALYSIS II. The Hermitian case (345K, Postscript) Mar 25, 03

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Abstract. This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case'' (to appear in the Annales de l'Institut Fourier, volume in honor of Fr d ric Pham). We consider here the case where the dispersion matrix is complex Hermitian. Under a natural transversality hypothesis, the manifold of crossings of two zero eigenvalue has codimension $4$. We study several cases: --The symplectic case --The corank $2$ case which splits into an elliptic case and an hyperbolic case --The case of systems with one degree of freedom depending on parameters. The methods are those of the first part, but the results are sometimes more complex.

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