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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2664

Title: New aspects in the unfolding of the nilpotent singularity of codimension three
Authors: DUMORTIER, Freddy
IBANEZ MESA, Santiago
KOKUBU, Hiroshi
Issue Date: 2001
Publisher: TAYLOR & FRANCIS LTD
Citation: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 16(1). p. 63-95
Abstract: This paper is concerned with three-dimensional vector fields and more specifically with the study of dynamics in unfoldings of the nilpotent singularity of codimension three. The ultimate goal is to understand the dynamics and bifurcations in the unfolding of the singularity. However, it is clear from the literature that the bifurcation diagram is very complicated and a complete study is far beyond the current possibilities, not only from a theoretical point of view but also from a numerical point of view, despite recent developments of computational methods for dynamical systems, Since all complicated dynamical behaviour is known to be of small amplitude, shrinking to the singularity for parameter values tending to the bifurcation parameter, the aim in this paper is especially to focus on a different aspect that might be interesting in the study of global bifurcation problems in the presence of such a nilpotent singularity of codimension three. The notion is introduced of-traffic regulator' and the specific sets called the 'inset' and 'outset', which give a new framework for studying a transition map in a cylindrical neighbourhood of the singularity that contains all the non-trivial dynamics that can bifurcate from the singularity, focusing on the domains on which the transition map is defined, A list is also given of open problems which are believed to be helpful for future investigation of the bifurcations from the nilpotent triple zero singularity in R-3.
Notes: Limburgs Univ Ctr, Dept Math, B-3590 Diepenbeek, Belgium. Univ Oviedo, Dept Math, Oviedo 33007, Spain. Kyoto Univ, Dept Math, Kyoto 6068502, Japan.Dumortier, F, Limburgs Univ Ctr, Dept Math, Univ Campus, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/2664
DOI: 10.1080/02681110010017417
ISI #: 000169354200003
ISSN: 1468-9367
Category: A1
Type: Journal Contribution
Validation: ecoom, 2002
Appears in Collections: Research publications

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