Normal resonances in a double Hopf bifurcation

Open Access
Authors
Publication date 02-2021
Journal Indagationes Mathematicae
Volume | Issue number 32 | 1
Pages (from-to) 33-54
Organisations
  • Faculty of Economics and Business (FEB) - Amsterdam School of Economics Research Institute (ASE-RI)
  • Faculty of Economics and Business (FEB)
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
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1-s2.0-S0019357720300951-main (Final published version)
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