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|Title: ||Homoclinic-doubling cascades|
|Authors: ||Homburg, AJ|
|Issue Date: ||2001|
|Citation: ||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.|
|ISI #: ||000172554400002|
|Type: ||Journal Contribution|
|Validation: ||ecoom, 2002|
|Appears in Collections: ||Research publications|
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