{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:21Z","timestamp":1740134541219,"version":"3.37.3"},"reference-count":16,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11226158","2011B110011"],"award-info":[{"award-number":["11226158","2011B110011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Henan","award":["11226158","2011B110011"],"award-info":[{"award-number":["11226158","2011B110011"]}]},{"name":"Doctor Fund of Henan University of Technology","award":["11226158","2011B110011"],"award-info":[{"award-number":["11226158","2011B110011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We define a Hofer-type norm for the Hamiltonian map on regular Poisson manifold and prove that it is nondegenerate. We show that the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msup><mml:mi>L<\/mml:mi><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mi>\u221e<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>-norm and the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msup><mml:mi>L<\/mml:mi><mml:mi>\u221e<\/mml:mi><\/mml:msup><\/mml:mrow><\/mml:math>-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<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>M<\/mml:mi><mml:mo>,<\/mml:mo><mml:mrow><mml:mo stretchy=\"false\">{<\/mml:mo><mml:mrow><mml:mo>\u00b7<\/mml:mo><mml:mo>,<\/mml:mo><mml:mo>\u00b7<\/mml:mo><\/mml:mrow><mml:mo stretchy=\"false\">}<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>by a compact Lie group Hamiltonian action is also compared.<\/jats:p>","DOI":"10.1155\/2014\/879196","type":"journal-article","created":{"date-parts":[[2014,3,30]],"date-time":"2014-03-30T04:01:32Z","timestamp":1396152092000},"page":"1-9","source":"Crossref","is-referenced-by-count":1,"title":["A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold"],"prefix":"10.1155","volume":"2014","author":[{"given":"Dawei","family":"Sun","sequence":"first","affiliation":[{"name":"College of Science, Henan University of Technology, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenxing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Nankai University, Tianjin 300071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"3","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500024549"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01444643"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700007410"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.2307\/2118524"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.difgeo.2008.04.005"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8540-9"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2682-6"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/S0040-9383(96)00024-9"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-94-07609-6"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572615"},{"key":"11a","doi-asserted-by":"publisher","DOI":"10.1007\/BF01231437"},{"key":"11b","doi-asserted-by":"publisher","DOI":"10.1007\/BF01231438"},{"issue":"4","key":"12","doi-asserted-by":"crossref","first-page":"579","DOI":"10.4310\/AJM.2002.v6.n4.a1","volume":"6","year":"2002","journal-title":"Asian Journal of Mathematics"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8299-6"},{"key":"1","series-title":"Mathematics and Its Applications","first-page":"xii+197","volume":"400","year":"1997"},{"key":"13","series-title":"Progress in Mathematics","first-page":"xxxiv+497","volume":"222","year":"2004"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/879196.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/879196.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/879196.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T06:37:53Z","timestamp":1498113473000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/879196\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":16,"alternative-id":["879196","879196"],"URL":"https:\/\/doi.org\/10.1155\/2014\/879196","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}