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Dulac Functions of Planar Vector Fields

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Abstract

In this work we give sufficient conditions for the existence of a Dulac function for an arbitrary differential system. This Dulac function allows to discard the existence of limit cycles in its domain of definition if this domain is a simply connected region. If the domain of definition is \(\ell \)-multiple connected then the Dulac function can estimate the number of limit cycles inside the domain.

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Acknowledgments

The author is partially supported by the MINECO/FEDER Grant number MTM2011–22877 and by an AGAUR (Generalitat de Catalunya) Grant number 2009SGR–381.

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  1. Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 , Lleida, Catalonia, Spain

    Jaume Giné

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  1. Jaume Giné
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Correspondence to Jaume Giné.

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Giné, J. Dulac Functions of Planar Vector Fields. Qual. Theory Dyn. Syst. 13, 121–128 (2014). https://doi.org/10.1007/s12346-014-0108-x

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  • DOI: https://doi.org/10.1007/s12346-014-0108-x

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