QUASIPERIODIC MATHIEU-HILL EQUATION.

Stephen H. Davis*, S. Rosenblat

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Scopus citations

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 languageEnglish (US)
Pages (from-to)139-155
Number of pages17
JournalSIAM Journal on Applied Mathematics
Volume38
Issue number1
DOIs
StatePublished - Jan 1 1980

ASJC Scopus subject areas

  • Applied Mathematics

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