Complex geometric asymptotics for nonlinear systems on complex varieties

Alber, M. S. and J. E. Marsden

Topol. Meth. in Nonlinear Anal., 4, (1994), 237-251


In this paper we describe the general method of complex geometric asymptotic and illustrate it by constructing semiclassical modes for three types of systems. The first type concerns families of geodesics on n -dimensional quadrics and in domains bounded by quadrics in the context of problems of diffraction. We also construct semiclassical modes for umbilic billiards and for the n -dimensional complex spherical pendulum. This last example also illustrates the phenomena of semiclassical monodromy.