A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold
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 geodes...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/879196 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |