On the persistence of quasi-periodic invariant tori for double Hopf bifurcation of vector fields

• Published in: Journal of Differential Equations Vol. 260; no. 10; pp. 7320 - 7357
• Main Author: Li, Xuemei
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.05.2016
• Subjects: Double Hopf bifurcation; KAM technique; Persistence; Quasi-periodic invariant torus; Persistence; KAM technique; Double Hopf bifurcation; Quasi-periodic invariant torus

We analyze the persistence of quasi-periodic invariant 2- and 3-tori for the double Hopf (Hopf–Hopf) bifurcation by using the KAM method. We prove that in a sufficiently small neighborhood of the bifurcation point, the full system has quasi-periodic 2-tori for most of the parameter sets where its tr...