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Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2009, Issue 2(68), Pages 26–32 (Mi vsgu220)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Rotation number like total characteristic of stability of Hill equation

A. A. Zhukova

Dept. of mathematics, informatics and mechanics Voronezh State University, Voronezh, 394036, Russia
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Abstract: Hill equation is considered. After transition to polar coordinates differential equation on torus for polar corner, satisfying to Karateodori conditions is gained. We shall give basic results.
Hill equation (with various multiplicators) is strongly stable (strongly unstable) then and only then, when the rotation number is nonintegral (integral) nonnegative number.
Formula connecting the nonintegral rotation number with multiplicators of Hill equation is received.
Keywords: strong stability, differential equations on torus, the number of rotation, multiplicators.
Received: 10.02.2009
Revised: 10.02.2009
Document Type: Article
UDC: 519.923.52
Language: Russian
Citation: A. A. Zhukova, “Rotation number like total characteristic of stability of Hill equation”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2009, no. 2(68), 26–32
Citation in format AMSBIB
\Bibitem{Zhu09}
\by A.~A.~Zhukova
\paper Rotation number like total characteristic of stability of Hill equation
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2009
\issue 2(68)
\pages 26--32
\mathnet{http://mi.mathnet.ru/vsgu220}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Самарского государственного университета. Естественнонаучная серия
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