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Smooth normal forms for integrable Hamiltonian systems near a focus–focus singularity

Acta Mathematica Vietnamica volume 38, pages 107–122 (2013)Cite this article

Abstract

We prove that completely integrable systems are normalizable in the C ∞ category near a focus–focus singularity.

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Notes

  1. p N+1≥p N .

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Authors and Affiliations

  1. IRMAR, Université de Rennes 1, 263 av. du Général Leclerc, 35042, Rennes Cedex, France

    San Vũ Ngọc & Christophe Wacheux

Authors
  1. San Vũ Ngọc
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  2. Christophe Wacheux
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Correspondence to Christophe Wacheux.

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Vũ Ngọc, S., Wacheux, C. Smooth normal forms for integrable Hamiltonian systems near a focus–focus singularity. Acta Math Vietnam. 38, 107–122 (2013). https://doi.org/10.1007/s40306-013-0012-5

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  • DOI: https://doi.org/10.1007/s40306-013-0012-5

Keywords

  • Integrable systems
  • Normal forms
  • Focus–focus singularities
  • Lagrangian foliations
  • Hamiltonian actions

Mathematics Subject Classification (2010)

  • 37J05
  • 53D12
  • 53D20
  • 70G60
  • 70H33