Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2908
Title: Chaotic dynamics in Z(2)-equivariant unfoldings of codimension three singularities of vector fields in R-3
Authors: DUMORTIER, Freddy 
KOKUBU, Hiroshi
Issue Date: 2000
Publisher: CAMBRIDGE UNIV PRESS
Source: ERGODIC THEORY AND DYNAMICAL SYSTEMS, 20(1). p. 85-107
Abstract: We study the most generic nilpotent singularity of a vector field in R-3 which is equivariant under reflection with respect to a line, say the z-axis. We prove the existence of eight equivalence classes for C-0-equivalence, all determined by the 2-jet. We also show that in certain cases, the Z(2)-equivariant unfoldings generically contain codimension one heteroclinic cycles which are comparable to the Skil'nikov-type homoclinic cycle in non-equivariant unfoldings. The heteroclinic cycles are accompanied by infinitely many horseshoes and also have a reasonable possibility of generating suspensions of Henon-Like attractors, and even Lorenz-like attractors.
Notes: Limburgs Univ Ctr, Dept Math, B-3590 Diepenbeek, Belgium. Kyoto Univ, Dept Math, Kyoto 6068502, Japan.Dumortier, F, Limburgs Univ Ctr, Dept Math, Univ Campus, B-3590 Diepenbeek, Belgium.
Document URI: http://hdl.handle.net/1942/2908
DOI: 10.1017/S0143385700000067
ISI #: 000086117800006
Category: A1
Type: Journal Contribution
Validations: ecoom 2001
Appears in Collections:Research publications

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