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nilpotent centre problem

European Journal of Applied Mathematics (1)

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Nilpotent centres via inverse integrating factors
ANTONIO ALGABA, CRISTÓBAL GARCÍA, JAUME GINÉ
Journal:

European Journal of Applied Mathematics / Volume 27 / Issue 5 / October 2016

Published online by Cambridge University Press:

23 March 2016, pp. 781-795
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In this paper, we are interested in the nilpotent centre problem of planar analytic monodromic vector fields. It is known that the formal integrability is not enough to characterize such centres. More general objects are considered as the formal inverse integrating factors. However, the existence of a formal inverse integrating factor is not sufficient to describe all the nilpotent centres. For the family studied in this paper, it is enough.