The center problem for degenerated monodromic critical points is far to be solved in general. In this paper we give a procedure to solve it for a particular perturbation of critical points which dominant part near the critical point is x2n-1∂/∂x + y2m-1∂/∂y. For these critical points the problem is solved by writing its associated differential equation in the generalized polar coordinates introduced by Lyapunov and by developing a new method of computation of the so called generalized Lyapunov contants. This method is based into the transformation of the differential equation into the perturbation of a Hamiltonian system. Finally, the method is applied to solve the center and the stability problem for a particular family of differential equations.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 1 Aug 2001|
- Center point
- Generalized Lyapunov constants