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

Dawei Sun and Zhenxing Zhang

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

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 L1,∞‐norm and the L∞‐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 (M, {·, ·}) by a compact Lie group Hamiltonian action is also compared.

Date: 2014
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https://doi.org/10.1155/2014/879196

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:879196

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