Cyclicity of a fake saddle inside the quadratic vector fields
de Maesschalck, Peter (Hasselt University (Belgium))
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Centre de Recerca per a l'Educació Científica i Matemàtica)

Date:	2015
Abstract:	This paper concerns the study of small-amplitude limit cycles that appear in the phase portrait near an unfolded fake saddle singularity. This degenerate singularity is also known as a impassable grain. The normal form of the unperturbed vector field is like a degenerate flow box. Near the singularity,the phase portrait consists of parallel fibers, all of which but one have no singular points, and at the singular fiber, there is one node. We study different techniques in order to show that the cyclicity is bigger or equal than two when the normal form is quadratic.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Note:	Agraïments: The first author acknowledges the support of FWO Vlaanderen (Grant number G093910). UNAB10-4E-378 grants
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Bifurcations ; Cyclicity ; Fake saddle ; Impassable grain ; Limit cycles
Published in:	Journal of differential equations, Vol. 258 Núm. 2 (2015) , p. 588-620, ISSN 1090-2732

DOI: 10.1016/j.jde.2014.09.024

Postprint 34 p, 509.4 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles