Normal-normal resonances in a double Hopf bifurcation

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.Comment: 22 pages, 6 figure

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    Last time updated on 18/10/2022