Regular and Chaotic Dynamics

, Volume 15, Issue 4–5, pp 532–550 | Cite as

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

Special Issue: Valery Vasilievich Kozlov-60

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.

Key words

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

MSC2000 numbers

22F05 35A30 35Q53 53A55 58A20 53D17 

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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