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Finite cyclicity of slow-fast Darboux systems with a two-saddle loop


Authors: Marcin Bobieński and Lubomir Gavrilov
Journal: Proc. Amer. Math. Soc. 144 (2016), 4205-4219
MSC (2010): Primary 34C08, 34M03, 34M35
DOI: https://doi.org/10.1090/proc/12678
Published electronically: June 10, 2016
MathSciNet review: 3531173
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Abstract: We prove that the cyclicity of a slow-fast integrable system of Darboux type with a double heteroclinic loop is finite and uniformly bounded.


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Additional Information

Marcin Bobieński
Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Email: mbobi@mimuw.edu.pl

Lubomir Gavrilov
Affiliation: Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France

DOI: https://doi.org/10.1090/proc/12678
Keywords: Slow-fast system, limit cycle, double heteroclinic loop
Received by editor(s): September 13, 2013
Received by editor(s) in revised form: October 13, 2014
Published electronically: June 10, 2016
Additional Notes: This research was supported by Polish NCN Grant No 2011/03/B/ST1/00330
Communicated by: Walter Van Assche
Article copyright: © Copyright 2016 American Mathematical Society