Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2662
Title: Homoclinic-doubling cascades
Authors: Homburg, AJ
KOKUBU, Hiroshi
NAUDOT, Vincent 
Issue Date: 2001
Publisher: SPRINGER-VERLAG
Source: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 160(3). p. 195-243
Abstract: Cascades of period-doubling bifurcation,; have attracted much interest from researchers of dynamical systems in the past two decades as they are one of the routes to onset of chaos. In this paper we consider routes to onset of chaos involving homoclinic-doubling bifurcations. We show the existence of cascades of homoclinic-doubling bifurcations which occur persistently in two-parameter families of vector fields on R-3. The cascades are found in an unfolding of a codimension-three homoclinic bifurcation which occur an orbit-flip at resonant eigenvalues. We develop a continuation theory for homoclinic orbits in order to follow homoclinic orbits through infinitely many homoclinic-doubling bifurcations.
Notes: Univ Amsterdam, Korteweg de Vries Inst Math, NL-1018 TV Amsterdam, Netherlands. Kyoto Univ, Dept Math, Kyoto 6068502, Japan. Limburgs Univ Ctr, Dept WNI, B-3590 Diepenbeek, Belgium.Homburg, AJ, Univ Amsterdam, Korteweg de Vries Inst Math, Plantage Muidergracht 24, NL-1018 TV Amsterdam, Netherlands.
Document URI: http://hdl.handle.net/1942/2662
ISSN: 0003-9527
e-ISSN: 1432-0673
DOI: 10.1007/s002050100159
ISI #: 000172554400002
Category: A1
Type: Journal Contribution
Validations: ecoom 2002
Appears in Collections:Research publications

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