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A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold

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  • Dawei Sun
  • Zhenxing Zhang

Abstract

We define a Hofer-type norm for the Hamiltonian map on regular Poisson manifold and prove that it is nondegenerate. We show that the -norm and the -norm coincide for the Hamiltonian map on closed regular Poisson manifold and give some sufficient conditions for a Hamiltonian path to be a geodesic. The norm between the Hamiltonian map and the induced Hamiltonian map on the quotient of Poisson manifold by a compact Lie group Hamiltonian action is also compared.

Suggested Citation

  • Dawei Sun & Zhenxing Zhang, 2014. "A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, March.
    • Handle: RePEc:hin:jnljam:879196
    DOI: 10.1155/2014/879196
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