Poisson structures for geometric curve flows in semi-simple homogeneous spaces

G. Marí Beffa, P. J. Olver

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We apply the equivariant method of moving frames to investigate the existence of Poisson structures for geometric curve flows in semi-simple homogeneous spaces. We derive explicit compatibility conditions that ensure that a geometric flow induces a Hamiltonian evolution of the associated differential invariants. Our results are illustrated by several examples of geometric interest.

Original languageEnglish (US)
Pages (from-to)532-550
Number of pages19
JournalRegular and Chaotic Dynamics
Volume15
Issue number4
DOIs
StatePublished - 2010

Bibliographical note

Funding Information:
The research of the second author was supported in part by NSF Grant DMS 08-07317.

Keywords

  • Poisson structure
  • differential invariant
  • homogeneous space
  • invariant curve flow
  • invariant variational bicomplex
  • moving frame

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