Direct decomposition of m(λ) matrices for hamiltonian systems

Abstract

The 2nd dimensional linear matrix Hamiltonian system has square integrable solutions given by , where γ is a fundamental matrix, provided M lies on a surface in complex space. If n=1, the surface is well known. It is a circle or a point. When n>1, the nature of the surface is relatively unknown. We show that the surface consists of the intersection of 2n (possibly degenerate)ellipsoidal cylinders. When n=1, in fact, the circle, mentioned above is actually the extremal of a one demensional ellipse in complex space.

AMS(MOS):

• 34A30
• 34B05
• 34B20
• 34B25

Keywords:

• Sturm-Liouville
• Weyl
• Hamiltonian systems
• boundary value problem