An algebraic approach to the center problem for ODEs 1
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
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.