Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3790
Title: ELEMENTARY GRAPHICS OF CYCLICITY-1 AND CYCLICITY-2
Authors: Roussarie, R
ROUSSEAU, C
DUMORTIER, Freddy 
Issue Date: 1994
Publisher: IOP PUBLISHING LTD
Source: NONLINEARITY, 7(3). p. 1001-1043
Abstract: In this paper we elaborate the techniques to prove for several elementary graphics that their cyclicity is one or two. We first prove two main results for C(infinity) vector fields in general. The first one states that a graphic through an arbitrary number of attracting hyperbolic saddles (hyperbolicity ratio r > 1) and attracting semi-hyperbolic points (one negative eigenvalue) has cyclicity 1. A second result says that for a graphic with one hyperbolic and one semi-hyperbolic singularity of opposite character the cyclicity is two. We then specialize to graphics with fixed connections and show that 33 graphics appearing among quadratic systems and listed in a previous paper have a cyclicity at most two (five cases are done only under generic conditions).
Notes: DEPT MATH,TOPOL LAB,URA 755,F-21004 DIJON,FRANCE. UNIV MONTREAL,DEPT MATH,MONTREAL H3C 3J7,QUEBEC,CANADA. UNIV MONTREAL,CRM,MONTREAL H3C 3J7,QUEBEC,CANADA.DUMORTIER, F, LIMBURGS UNIV CENTRUM,UNIV CAMPUS,B-3610 DIEPENBEEK,BELGIUM.
Document URI: http://hdl.handle.net/1942/3790
ISI #: A1994NN64900013
Type: Journal Contribution
Appears in Collections:Research publications

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