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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2569

Title: Normal forms near a saddle-node and applications to finite cyclicity of graphics
Authors: DUMORTIER, Freddy
Ilyashenko, Y
Rousseau, C
Issue Date: 2002
Publisher: CAMBRIDGE UNIV PRESS
Citation: ERGODIC THEORY AND DYNAMICAL SYSTEMS, 22. p. 783-818
Abstract: We refine the transformation to smooth normal form for an analytic family of vector fields in the neighbourhood of a saddle-node. This refinement is very powerful and allows us to prove the finite cyclicity of families of graphics ('ensembles') occurring inside analytic families of vector fields. In [ZR1] and [ZR2] it is used to prove the finite cyclicity of graphics through a nilpotent singular point of elliptic type. Several examples are presented: lips, graphics with two subsequent lips, graphics with a nilpotent point of elliptic type and a saddle-node. We also discuss the bifurcation diagram of limit cycles for a graphic in the lips.
Notes: Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium. Cornell Univ, Dept Math, Ithaca, NY 14853 USA. State & Independent Moscow Univ, VA Steklov Math Inst, Moscow 117333, Russia. Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada. Univ Montreal, CRM, Montreal, PQ H3C 3J7, Canada.Dumortier, F, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/2569
DOI: 10.1017/S0143385702000391
ISI #: 000176290700008
ISSN: 0143-3857
Category: A1
Type: Journal Contribution
Validation: ecoom, 2003
Appears in Collections: Research publications

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