Abstract
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.
Original language | English (US) |
---|---|
Pages (from-to) | 565-589 |
Number of pages | 25 |
Journal | Nonlinearity |
Volume | 26 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2013 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics