About the Poincaré-Lyapunov theorem and necessary conditions for the existence of a center (Q1032836)
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scientific article; zbMATH DE number 5625412
| Language | Label | Description | Also known as |
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| English | About the Poincaré-Lyapunov theorem and necessary conditions for the existence of a center |
scientific article; zbMATH DE number 5625412 |
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About the Poincaré-Lyapunov theorem and necessary conditions for the existence of a center (English)
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5 November 2009
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The center-focus problem is revisited for planar analytic vector fields using the matricial formulation, and a direct computational method is given for sufficient conditions of a center. The method is applied to systems with a linear center perturbed by homogeneous polynomials giving the first necessary conditions. A simple proof of the Poincaré-Lyapunov theorem is also given.
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planar analytic vector fields
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center-focus problem
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Poincaré-Lyapunov theorem
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