### Abstract

A study is mde of a generalized Mathieu-Hill equation u double prime plus left bracket delta plus epsilon (cos 2t plus alpha cos 2( lambda plus epsilon )t) right bracket u equals 0, where delta , epsilon , alpha , lambda are constants, with vertical epsilon vertical very much less than 1 and lambda a rational fraction. The equation has a quasiperiodic coefficient and Floquet theory is inapplicable. It is shown that a multiple scaling technique enables the stability characteristics of the equation to be calculated and the transition curves between stable and unstable regions of the epsilon - delta plane to be compared. The structure of the analysis is such that the small divisor problem is not encountered.

Original language | English (US) |
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Pages (from-to) | 139-155 |

Number of pages | 17 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 38 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1980 |

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

*SIAM Journal on Applied Mathematics*,

*38*(1), 139-155. https://doi.org/10.1137/0138012