Pseudo-abelian integrals on slow-fast Darboux systems  [ Intégrales pseudo-abéliennes sur des systèmes lent-rapide de Darboux ]
Annales de l'Institut Fourier, Tome 63 (2013) no. 2, p. 417-430
Nous étudions les intégrales pseudo-abéliennes associées aux déformations polynomiales des systèmes lent-rapide Darboux-intégrables. Sous certaines hypothèses, nous montrons l’existence d’une borne uniforme de leur nombre de zéros.
We study pseudo-abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number of their zeros.
DOI : https://doi.org/10.5802/aif.2765
Classification:  34C08,  70K70,  34C07
Mots clés: intégrales pseudo-abéliennes, intégrales abéliennes, systèmes lent-rapide, intégrabilité de Darboux, bifurcations, cycles limites
@article{AIF_2013__63_2_417_0,
     author = {Bobie\'nski, Marcin and Marde\v si\'c, Pavao and Novikov, Dmitry},
     title = {Pseudo-abelian integrals on slow-fast Darboux systems},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {2},
     year = {2013},
     pages = {417-430},
     doi = {10.5802/aif.2765},
     mrnumber = {3112517},
     zbl = {1278.34031},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2013__63_2_417_0}
}
Bobieński, Marcin; Mardešić, Pavao; Novikov, Dmitry. Pseudo-abelian integrals on slow-fast Darboux systems. Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 417-430. doi : 10.5802/aif.2765. http://www.numdam.org/item/AIF_2013__63_2_417_0/

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