Pseudo-abelian integrals on slow-fast Darboux systems
[Intégrales pseudo-abéliennes sur des systèmes lent-rapide de Darboux]
Bobieński, Marcin1 ; Mardešić, Pavao2 ; Novikov, Dmitry3
1 Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
2 Université de Bourgogne, Institut de Mathématiques de Bourgogne, U.M.R. 5584 du C.N.R.S., B.P. 47870, 21078 Dijon Cedex - France
3 Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 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 : 10.5802/aif.2765
Classification : 34C08, 70K70, 34C07
Keywords: pseudo-abelian integrals, abelian integrals, slow-fast systems, Darboux integrability, bifurcations, limit cycles
Mot clés : intégrales pseudo-abéliennes, intégrales abéliennes, systèmes lent-rapide, intégrabilité de Darboux, bifurcations, cycles limites
Bobieński, Marcin 1 ; Mardešić, Pavao 2 ; Novikov, Dmitry 3

1 Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
2 Université de Bourgogne, Institut de Mathématiques de Bourgogne, U.M.R. 5584 du C.N.R.S., B.P. 47870, 21078 Dijon Cedex - France
3 Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel 
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     title = {Pseudo-abelian integrals on slow-fast {Darboux} systems},
     journal = {Annales de l'Institut Fourier},
     pages = {417--430},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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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/articles/10.5802/aif.2765/

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