Geodesic flows on diffeomorphism groups with Sobolev metrics and integrable systems

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Abstract

The Harry-Dym equation comes from geodesic flows on diffeomorphism groups. This fact has been observed before by the Marsden school. In this paper we show that the supersymmetric Harry-Dym equation arises from the geodesic flow on the supercon-formal group. We also show that the stabilizer of a point in the coad-joint representation of the Virasoro algebra endowed with a Sobolev norm consists of a space of projective vector fields. We also show that for each projective vector field, there exists a quadratic that satisfies a Neumann system.

Original languageBritish English
Pages (from-to)529-545
Number of pages17
JournalJournal of Dynamical and Control Systems
Volume8
Issue number4
DOIs
StatePublished - Oct 2002

Keywords

  • Bott-Virasoro group
  • Diffeomorphism
  • Dym equation
  • Geodesic flows

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