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

Dawei Sun | Zendy; Zhenxing Zhang | Zendy

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

Author(s) -

Dawei Sun,

Zhenxing Zhang

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/879196

Subject(s) - algorithm , hamiltonian (control theory) , artificial intelligence , computer science , mathematics , mathematical optimization

We define a Hofer-type norm for the Hamiltonian map on regular Poissonmanifold and prove that it is nondegenerate. We show that the L1,∞-norm and the L∞-normcoincide for the Hamiltonian map on closed regular Poisson manifold and give some sufficientconditions for a Hamiltonian path to be a geodesic. The norm between the Hamiltonian mapand the induced Hamiltonian map on the quotient of Poisson manifold (M,{·,·}) by a compact Lie group Hamiltonian action is also compared

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