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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
Citation: 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.
URI: http://hdl.handle.net/1942/18093
DOI: 10.1016/j.jde.2014.09.024
ISI #: 000345488200013
ISSN: 0022-0396
Category: A1
Type: Journal Contribution
Validation: ecoom, 2015
Appears in Collections: Research publications

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