Resonance and Singularities

  • Henk W. BroerEmail author
  • Gert Vegter
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 54)


The phenomenon of resonance will be dealt with from the viewpoint of dynamical systems depending on parameters and their bifurcations. Resonance phenomena are associated to open subsets in the parameter space, while their complement corresponds to quasi-periodicity and chaos. The latter phenomena occur for parameter values in fractal sets of positive measure. We describe a universal phenomenon that plays an important role in modelling. This paper gives a summary of the background theory, veined by examples.


Hopf Bifurcation Rotation Number Invariant Circle Sacker Bifurcation Drive Oscillator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author thanks Konstantinos Efstathiou, Aernout van Enter and Ferdinand Verhulst for their help in the preparation of this paper.


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Authors and Affiliations

  1. 1.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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