{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:36:24Z","timestamp":1753886184992,"version":"3.41.2"},"reference-count":22,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,6,19]],"date-time":"2011-06-19T00:00:00Z","timestamp":1308441600000},"content-version":"vor","delay-in-days":169,"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":["10871218","10932002"],"award-info":[{"award-number":["10871218","10932002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10871218","10932002"],"award-info":[{"award-number":["10871218","10932002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We characterize the geometry of the Hamiltonian\ndynamics with a conformal metric. After investigating the Eisenhart metric, we study\nthe corresponding conformal metric and obtain the geometric structure of the classical\nHamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the\nJacobi field along the geodesics, and the equations for a certain flow constrained in a family\nof conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures,\nthe geodesic equations, the Jacobi equations, and the equations for the flow of the\nfamous models, an <jats:italic>N<\/jats:italic> degrees of freedom linear Hamiltonian system and the H\u00e9non\u2010Heiles\nmodel are given, and in a special case, numerical solutions of the conformal geodesics, the\ngeneralized momenta, and the Jacobi field along the geodesics of the H\u00e9non\u2010Heiles model\nare obtained. And the numerical results for the H\u00e9non\u2010Heiles model show us the instability\nof the associated geodesic spreads.<\/jats:p>","DOI":"10.1155\/2011\/710274","type":"journal-article","created":{"date-parts":[[2011,6,19]],"date-time":"2011-06-19T19:35:10Z","timestamp":1308512110000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric"],"prefix":"10.1155","volume":"2011","author":[{"given":"Linyu","family":"Peng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huafei","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,6,19]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0370\u20101573(00)00069\u20107"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2011.04.016"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305\u20104470\/38\/25\/008"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1474-6670(17)38866-3"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01085489"},{"key":"e_1_2_7_6_2","series-title":"Itogi Nauki i Tekhniki","first-page":"59","volume-title":"Problems in Geometry","author":"Ferapontov E. 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Ricci deformation and conformal change of metrics IC\/99\/89 1999 International Centre for Theoretical Physics Trieste Italy."},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.02.002"},{"volume-title":"Gravitation","year":"1973","author":"Misner C. W.","key":"e_1_2_7_17_2"},{"key":"e_1_2_7_18_2","doi-asserted-by":"publisher","DOI":"10.4310\/jdg\/1214436922"},{"key":"e_1_2_7_19_2","series-title":"Texts in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-2682-6","volume-title":"Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems","author":"Marsden J. E.","year":"1994"},{"key":"e_1_2_7_20_2","first-page":"591","article-title":"Dynamical trajectories and geodesics","volume":"30","author":"Eisenhart L. P.","year":"1929","journal-title":"Annals of Mathematics(Princeton)"},{"key":"e_1_2_7_21_2","doi-asserted-by":"crossref","unstructured":"GurzadyanV. G. Chaotic phenomena in astrophysics and cosmology Proceedings of the 10th Brazilian School of Cosmology and Gravitation July-August 2002.","DOI":"10.1142\/9789812777386_0014"},{"key":"e_1_2_7_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.2722"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2011\/710274.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2011\/710274.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2011\/710274","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T13:44:36Z","timestamp":1718027076000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2011\/710274"}},"subtitle":[],"editor":[{"given":"Heinrich","family":"Begehr","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1155\/2011\/710274"],"URL":"https:\/\/doi.org\/10.1155\/2011\/710274","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2011,1]]},"assertion":[{"value":"2010-12-03","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-04-12","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-06-19","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"710274"}}