Normal resonances in a double Hopf bifurcation
| Authors |
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| Publication date | 02-2021 |
| Journal | Indagationes Mathematicae |
| Volume | Issue number | 32 | 1 |
| Pages (from-to) | 33-54 |
| Organisations |
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| Abstract | We introduce a framework to systematically investigate the resonant double Hopf bifurcation. We use the basic invariants of the ensuing T^1-action to analyse the approximating normal form truncations in a unified manner. In this way we obtain a global description of the parameter space and thus find the organising resonance droplet, which is the present analogue of the resonant gap. The dynamics of the normal form yields a skeleton for the dynamics of the original system. In the ensuing perturbation theory both normal hyperbolicity (centre manifold theory) and kam theory are being used. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1016/j.indag.2020.09.003 |
| Downloads |
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