This paper deals with large scale aspects of Hills equation ẍ +(a+bp(t))x = 0, where p is periodic with a fixed period. In particular, the interest is the asymptotic radial density of the stability domain in the (a, b)-plane. It turns out that this density changes discontinuously in a certain direction and exhibits and interesting asymptotic fine structure. Most of the paper deals with the case where p is a Morse function with one maximum and one minimum, but also the discontinuous case of square Hills equation is studied, where the density behaves differently.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics