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VARIATIONAL EQUATIONS OF HIGHER ORDER IN THE CENTER-FOCUS PROBLEM

    https://doi.org/10.1142/9789812794253_0134Cited by:1 (Source: Crossref)
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    Abstract:

    We consider an approach to the classical center-focus problem. For the wide class of systems with analytical right hand sides, the necessary and sufficient conditions for the center are given, which are expressed through the variational equations of higher order. The necessary conditions for the center are obtained along with the asymptotics of the Poincaré mapping in case of the focus. The effectiveness of the suggested method is demonstrated on some examples.