no. 2
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 
@article{AIF_2013__63_2_417_0,
     author = {Bobie\'nski, Marcin and Marde\v{s}i\'c, Pavao and Novikov, Dmitry},
     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},
     volume = {63},
     number = {2},
     year = {2013},
     doi = {10.5802/aif.2765},
     zbl = {1278.34031},
     mrnumber = {3112517},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2765/}
}
TY  - JOUR
AU  - Bobieński, Marcin
AU  - Mardešić, Pavao
AU  - Novikov, Dmitry
TI  - Pseudo-abelian integrals on slow-fast Darboux systems
JO  - Annales de l'Institut Fourier
PY  - 2013
SP  - 417
EP  - 430
VL  - 63
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.2765/
DO  - 10.5802/aif.2765
LA  - en
ID  - AIF_2013__63_2_417_0
ER  - 
%0 Journal Article
%A Bobieński, Marcin
%A Mardešić, Pavao
%A Novikov, Dmitry
%T Pseudo-abelian integrals on slow-fast Darboux systems
%J Annales de l'Institut Fourier
%D 2013
%P 417-430
%V 63
%N 2
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.2765/
%R 10.5802/aif.2765
%G en
%F 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/articles/10.5802/aif.2765/

[1] Bobieński, M. Pseudo-Abelian integrals along Darboux cycles: a codimension one case, J. Diff. Eq., Volume 246 (2009) no. 3, pp. 1364-1373 | DOI | MR | Zbl

[2] Bobieński, M.; Mardešić, P. Pseudo-Abelian integrals along Darboux cycles, Proc. Lond. Math. Soc. (3), Volume 97 (2008) no. 3, pp. 669-688 | DOI | MR | Zbl

[3] Bobieński, M.; Mardešić, P.; Novikov, D. Pseudo-abelian integrals: unfolding generic exponential, J. Diff. Eq., Volume 247 (2009) no. 12, pp. 3357-3376 | DOI | MR | Zbl

[4] Dumortier, F.; Roussarie, R. Canard cycles and center manifolds, 121, no 577, Mem. Amer. Math. Soc., 1996 | MR | Zbl

[5] Dumortier, F.; Roussarie, R. Multiple canard cycles in Generalized Liénard equations, J. Diff. Eq., Volume 174 (2001), pp. 1-29 | DOI | MR | Zbl

[6] Dumortier, F.; Roussarie, R. Abelian integrals and limit cycles, J. Diff. Eq., Volume 227 (2006) no. 1, pp. 116-165 | DOI | MR | Zbl

[7] Novikov, D. On limit cycles appearing by polynomial perturbation of Darbouxian integrable systems, Geom. Funct. Anal., Volume 18 (2009) no. 5, pp. 1750-1773 | DOI | MR | Zbl

Cité par Sources :