Abstract
We study pseudo-Abelian integrals associated with polynomial perturbations of Darboux integrable system with a triple point. Under some assumptions, we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-Abelian integrals is bounded uniformly for nearby Darboux integrable foliations.
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Acknowledgments
It is a pleasure to thank Pavao Mardešić (Université de Bourgogne-Dijon) and Daniel Panazzolo (Université de Haute Alsace-Mulhouse) for their constant support in this work. The author is very much indebted to the anonymous referee for the careful reading of this manuscript and the valuable comment.
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Braghtha, A. Darboux Integrable System with a Triple Point and Pseudo-Abelian Integrals. J Dyn Control Syst 26, 761–774 (2020). https://doi.org/10.1007/s10883-020-09477-3
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DOI: https://doi.org/10.1007/s10883-020-09477-3