Deformations of Poisson structures on fibered manifolds and adiabatic slow-fast systems

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Abstract

In the context of normal forms, we study a class of slow-fast Hamiltonian systems on general Poisson fiber bundles with symmetry. Our geometric approach is motivated by a link between the deformation theory for Poisson structures on fibered manifolds and the adiabatic perturbation theory. We present some normalization results which are based on the averaging theorem for horizontal 2-cocycles on Poisson fiber bundles.

Original languageEnglish
Article number1750086
JournalInternational Journal of Geometric Methods in Modern Physics
Volume14
Issue number6
DOIs
StatePublished - 1 Jun 2017

Bibliographical note

Publisher Copyright:
© 2017 World Scientific Publishing Company.

Keywords

  • Poisson cohomology
  • Poisson fiber bundle
  • adiabatic approximation
  • deformation theory
  • normal forms

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