Integrability and limit cycles for Abel equations

Tom 94 / 2011

Jean-Pierre Françoise Banach Center Publications 94 (2011), 187-196 MSC: Primary 34C29; Secondary 34C25, 58F22. DOI: 10.4064/bc94-0-11


Abel equations are among the most natural ordinary differential equations which have a Godbillon-Vey sequence of length 4. We show that the associated Poincaré mapping can be expressed by iterated integrals with three functions which are solutions of a system of partial differential equations.


  • Jean-Pierre FrançoiseLaboratoire J.-L. Lions
    UMR 7598, CNRS
    Université P.-M. Curie, Paris 6
    75005 Paris, France

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