Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/18093
Title: Cyclicity of a fake saddle inside the quadratic vector fields
Authors: DE MAESSCHALCK, Peter 
Rebollo-Perdomo, S.
Torregrosa, J.
Issue Date: 2015
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 258 (2), p. 588-620
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 an impassable grain. The canonical form of the unperturbed vector field is like a degenerate flow box. Near the singularity, the phase portrait consists of parallel fibers, all but one of which have no singular points, and at the singular fiber, there is one node. We demonstrate different techniques in order to show that the cyclicity is bigger than or equal to two when the canonical form is quadratic. (C) 2014 Elsevier Inc. All rights reserved.
Notes: [De Maesschalck, P.] Hasselt Univ, B-3500 Hasselt, Belgium. [Rebollo-Perdomo, S.] Ctr Recerca Matemat, Barcelona 08193, Spain. [Torregrosa, J.] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain.
Keywords: cyclicity; fake saddle; impassable grain; limit cycle; bifurcation; singularity unfolding;Cyclicity; Fake saddle; Impassable grain; Limit cycle; Bifurcation; Singularity unfolding
Document URI: http://hdl.handle.net/1942/18093
ISSN: 0022-0396
e-ISSN: 1090-2732
DOI: 10.1016/j.jde.2014.09.024
ISI #: 000345488200013
Rights: © 2014 Elsevier Inc. All rights reserved.
Category: A1
Type: Journal Contribution
Validations: ecoom 2015
Appears in Collections:Research publications

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