Normal-normal resonances in a double Hopf bifurcation

2020/01/24 by Henk Broer, Broer, Henk, Heinz Hanßmann +4
Computer Science · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2001.08916

openalex publication_date 2020/01/24 · openalex created_date 2025/11/01 · openalex updated_date 2026/08/01

Abstract

We investigate the stability loss of invariant n-dimensional quasi-periodic tori during a double Hopf bifurcation, where at bifurcation the two normal frequencies are in normal-normal resonance. Invariants are used to analyse the normal form approximations in a unified manner. The corresponding dynamics form a skeleton for the dynamics of the original system. Here both normal hyperbolicity and KAM theory are being used.

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