- 03-135 COLIN de VERDIERE Yves
- THE LEVEL CROSSING PROBLEM IN SEMI-CLASSICAL ANALYSIS
II. The Hermitian case
Mar 25, 03
(auto. generated ps),
of related papers
Abstract. This paper is the second part of
``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
The methods are those of the first part, but the results
are sometimes more complex.