alexa An algebraic approach to the center problem for ODEs 1
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

An algebraic approach to the center problem for ODEs 1

Alexander BRUDNYI

Department of Mathematics and Statistics, University of Calgary,
2500 University Drive NW, T1N 1N4 Calgary, Canada

E-mail: [email protected]

Received date: December 14, 2007; Revised date:March 07, 2008

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The classical Poincar´e Center-Focus problem asks about the characterization of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point, a center. This problem is reduced to a center problem for certain ODE . We present an algebraic approach to the center problem based on the study of the group of paths determined by the coefficients of the ODE.

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