Asymptotic Solutions of a Hamiltonian System in Intervals with Several Turning Points
Harry Gingold, Po-Fang Hsieh · SIAM Journal on Mathematical Analysis · 1988
The global asymptotic decomposition of a Hamiltonian system $i\varepsilon Y' = H(x)Y$, as $\varepsilon \to 0^ + $, is studied. Here $H(x)$ is a Hermitian matrix analytic on $I = [a,b]$ where a could be $- \infty$ and b could be $\infty $. Furthermore, I may contain several turning points with various orders of this system. A complete decomposition for the asymptotic solutions is also given.