Pseudo-abelian integrals on slow-fast Darboux systems

Marcin Bobieński[1]; Pavao Mardešić[2]; Dmitry Novikov[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

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 2, page 417-430
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Bobieński, Marcin, Mardešić, Pavao, and Novikov, Dmitry. "Pseudo-abelian integrals on slow-fast Darboux systems." Annales de l’institut Fourier 63.2 (2013): 417-430. <http://eudml.org/doc/275452>.

@article{Bobieński2013,
abstract = {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.},
affiliation = {Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland; Université de Bourgogne, Institut de Mathématiques de Bourgogne, U.M.R. 5584 du C.N.R.S., B.P. 47870, 21078 Dijon Cedex - France; Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel},
author = {Bobieński, Marcin, Mardešić, Pavao, Novikov, Dmitry},
journal = {Annales de l’institut Fourier},
keywords = {pseudo-abelian integrals; abelian integrals; slow-fast systems; Darboux integrability; bifurcations; limit cycles},
language = {eng},
number = {2},
pages = {417-430},
publisher = {Association des Annales de l’institut Fourier},
title = {Pseudo-abelian integrals on slow-fast Darboux systems},
url = {http://eudml.org/doc/275452},
volume = {63},
year = {2013},
}

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
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 2
SP - 417
EP - 430
AB - 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.
LA - eng
KW - pseudo-abelian integrals; abelian integrals; slow-fast systems; Darboux integrability; bifurcations; limit cycles
UR - http://eudml.org/doc/275452
ER -

References

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  1. M. Bobieński, Pseudo-Abelian integrals along Darboux cycles: a codimension one case, J. Diff. Eq. 246 (2009), 1364-1373 Zbl1163.34022MR2474594
  2. M. Bobieński, P. Mardešić, Pseudo-Abelian integrals along Darboux cycles, Proc. Lond. Math. Soc. (3) 97 (2008), 669-688 Zbl1171.34023MR2448243
  3. M. Bobieński, P. Mardešić, D. Novikov, Pseudo-abelian integrals: unfolding generic exponential, J. Diff. Eq. 247 (2009), 3357-3376 Zbl1197.34046MR2571581
  4. F. Dumortier, R. Roussarie, Canard cycles and center manifolds, 121, no 577 (1996), Mem. Amer. Math. Soc. Zbl0851.34057MR1327208
  5. F. Dumortier, R. Roussarie, Multiple canard cycles in Generalized Liénard equations, J. Diff. Eq. 174 (2001), 1-29 Zbl1024.34038MR1844521
  6. F. Dumortier, R. Roussarie, Abelian integrals and limit cycles, J. Diff. Eq. 227 (2006), 116-165 Zbl1111.34028MR2233957
  7. D. Novikov, On limit cycles appearing by polynomial perturbation of Darbouxian integrable systems, Geom. Funct. Anal. 18 (2009), 1750-1773 Zbl1167.32005MR2481741

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