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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/13216

Title: Cyclicity of common slow-fast cycles
Authors: De Maesschalck, Peter
Dumortier, Freddy
Roussarie, Robert
Issue Date: 2011
Citation: INDAGATIONES MATHEMATICAE-NEW SERIES, 22 (3-4), p. 165-206
Abstract: We study the limit cycles of planar slow–fast vector fields, appearing near a given slow–fast cycle, formed by an arbitrary sequence of slow parts and fast parts, and where the slow parts can meet the fast parts in a nilpotent contact point of arbitrary order. Using the notion slow divergence integral, we delimit a large subclass of these slow–fast cycles out of which at most one limit cycle can perturb, and a smaller subclass out of which exactly one limit cycle will perturb. Though the focus lies on common slow–fast cycles, i.e. cycles with only attracting or only repelling slow parts, we present results that are valid for more general slow–fast cycles. We also provide examples of attracting common slow–fast cycles out of which more than one limit cycle can perturb, one of which is repelling.
URI: http://hdl.handle.net/1942/13216
DOI: 10.1016/j.indag.2011.09.008
ISI #: 000298072500006
ISSN: 0019-3577
Category: A1
Type: Journal Contribution
Validation: ecoom, 2013
Appears in Collections: Research publications

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