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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/879196 |
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| _version_ | 1832553265806442496 |
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| author | Dawei Sun Zhenxing Zhang |
| author_facet | Dawei Sun Zhenxing Zhang |
| author_sort | Dawei Sun |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-73067059e1fa48a0970c889248e1f1b1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-73067059e1fa48a0970c889248e1f1b12025-02-03T05:54:29ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/879196879196A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson ManifoldDawei Sun0Zhenxing Zhang1College of Science, Henan University of Technology, Zhengzhou 450001, ChinaSchool of Mathematical Sciences, Nankai University, Tianjin 300071, ChinaWe 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.http://dx.doi.org/10.1155/2014/879196 |
| spellingShingle | Dawei Sun Zhenxing Zhang A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold Journal of Applied Mathematics |
| title | A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold |
| title_full | A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold |
| title_fullStr | A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold |
| title_full_unstemmed | A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold |
| title_short | A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold |
| title_sort | hofer type norm of hamiltonian maps on regular poisson manifold |
| url | http://dx.doi.org/10.1155/2014/879196 |
| work_keys_str_mv | AT daweisun ahofertypenormofhamiltonianmapsonregularpoissonmanifold AT zhenxingzhang ahofertypenormofhamiltonianmapsonregularpoissonmanifold AT daweisun hofertypenormofhamiltonianmapsonregularpoissonmanifold AT zhenxingzhang hofertypenormofhamiltonianmapsonregularpoissonmanifold |