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Bifurcations of normally parabolic tori in Hamiltonian systems

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Published 13 May 2005 • 2005 IOP Publishing Ltd and London Mathematical Society
, , Citation Henk W Broer et al 2005 Nonlinearity 18 1735 DOI 10.1088/0951-7715/18/4/018

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Author affiliations

1 Instituut voor Wiskunde en Informatica, Rijksuniversiteit Groningen, Blauwborgje 3, 9747 AC Groningen, The Netherlands

2 Institut für Reine und Angewandte Mathematik der RWTH Aachen, 52056 Aachen, Germany

3 Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China

4 Present address: Mathematisch Instituut, Universiteit Utrecht, Postbus 80010, 3508 TA Utrecht, The Netherlands.

Dates

  1. Received 30 November 2004
  2. Published

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0951-7715/18/4/1735

Abstract

We consider perturbations of integrable Hamiltonian systems in the neighbourhood of normally parabolic invariant tori. Under appropriate transversality conditions the tori in the unperturbed system bifurcate according to a (generalized) cuspoid catastrophe. Combining techniques of KAM theory and singularity theory, we show that such bifurcation scenarios survive the perturbation on large Cantor sets. Applications to rigid body dynamics and forced oscillators are pointed out.

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10.1088/0951-7715/18/4/018