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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 2, Pages 373–387 (Mi smj2091)  

A canonical system of two differential equations with periodic coefficients and the Poincaré–Denjoy theory of differential equations on a torus

A. I. Perov

Voronezh State University, Faculty of Applied Mathematics, Informatics and Mechanics, Voronezh
References:
Abstract: The passage from Cartesian to polar coordinates in a canonical system with periodic coefficients gives rise to a nonlinear differential equation whose right-hand side is periodic in time and the polar angle and thus this equation can be regarded as a differential equation on a torus. In accord with Poincaré–Denjoy theory, the behavior of a solution to a differential equation on a torus is characterized by the rotation number and some homeomorphic mapping of a circle onto itself. We study connections of strong stability (instability) of a canonical system, including the membership in the nth stability (instability) domain, with the rotation number and fixed points of this mapping.
Keywords: canonical system, Floquet multiplier, domains of strong stability, Poincaré–Denjoy theory, rotation number.
Received: 27.03.2008
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 2, Pages 301–312
DOI: https://doi.org/10.1007/s11202-010-0031-6
Bibliographic databases:
Document Type: Article
UDC: 517.926
Language: Russian
Citation: A. I. Perov, “A canonical system of two differential equations with periodic coefficients and the Poincaré–Denjoy theory of differential equations on a torus”, Sibirsk. Mat. Zh., 51:2 (2010), 373–387; Siberian Math. J., 51:2 (2010), 301–312
Citation in format AMSBIB
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\paper A canonical system of two differential equations with periodic coefficients and the Poincar\'e--Denjoy theory of differential equations on a~torus
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\yr 2010
\vol 51
\issue 2
\pages 373--387
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\jour Siberian Math. J.
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\issue 2
\pages 301--312
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    Сибирский математический журнал Siberian Mathematical Journal
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