×

Continuous dependence on parameters in the Hopf-Takens bifurcation of codimension 3. (Dépendance continue par rapport aux paramètres dans la bifurcation de Hopf-Takens de codimension 3.) (French) Zbl 0810.58025

Summary: The paper shows how to construct a \((C^ 0 - C^ 0)\)-equivalence, that means a \(C^ 0\)-equivalence depending continuously on parameters, between two generic Hopf-Takens bifurcations of codimension 2 and 3. It also includes the \((C^ 0 - C^ 0)\) study of the generic 2-parameter unfolding of the triple cycle.

MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[1] Newhouse, S.), Palis, N.) and Takens, F.) .- Bifurcations and stability of families of diffeomorphisms, Publ. Math. I.H.E.S., 57, pp. 5-72. · Zbl 0518.58031
[2] Palis, N.) and Roussarie, R.) .- Topological invariants as number of translation, , 1125 (1984) pp. 64-86. · Zbl 0575.58026
[3] Roussarie, R.) .- Weak and continuous equivalences for families on line diffeomorphisms, In M.I. Camacho, M.J. Pacifico & F. Takens. Dynamical Systems and bifurcation theory. 160 (1987) pp. 377-385. · Zbl 0641.58037
[4] Takens, F.) .- Unfoldings of certain Singularities of vectorfields, Generalised Hopf bifurcationsJ. Diff. Eq.14 (1973) pp. 476-493. · Zbl 0273.35009
[5] Yoccoz, J. Ch.) .- Centralisateurs et conjuguaison différentiable des difféomorphismes du cercle, Thèse, Université d’Orsay (1985).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.