Large scale radial stability density of Hill's equation

Henk Broer, Mark Levi, Carles Simo

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)565-589
Number of pages25
Issue number2
StatePublished - Feb 2013

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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