### 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) |
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Pages (from-to) | 565-589 |

Number of pages | 25 |

Journal | Nonlinearity |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2013 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

Broer, H., Levi, M., & Simo, C. (2013). Large scale radial stability density of Hill's equation.

*Nonlinearity*,*26*(2), 565-589. https://doi.org/10.1088/0951-7715/26/2/565