{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T20:52:07Z","timestamp":1757451127753,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,1,4]],"date-time":"2018-01-04T00:00:00Z","timestamp":1515024000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,1,4]],"date-time":"2018-01-04T00:00:00Z","timestamp":1515024000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["26287023"],"award-info":[{"award-number":["26287023"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s00332-017-9440-z","type":"journal-article","created":{"date-parts":[[2018,1,4]],"date-time":"2018-01-04T10:10:08Z","timestamp":1515060608000},"page":"1043-1077","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Toroidal Geometry Stabilizing a Latitudinal Ring of Point Vortices on a Torus"],"prefix":"10.1007","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4290-0942","authenticated-orcid":false,"given":"Takashi","family":"Sakajo","sequence":"first","affiliation":[]},{"given":"Yuuki","family":"Shimizu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,1,4]]},"reference":[{"key":"9440_CR1","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1007\/BF01090320","volume":"6","author":"VA Bogomolov","year":"1977","unstructured":"Bogomolov, V.A.: Dynamics of vorticity at a sphere. Fluid Dyn. 6, 863\u2013870 (1977)","journal-title":"Fluid Dyn."},{"key":"9440_CR2","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1103\/PhysRevLett.72.681","volume":"72","author":"A Corrada-Emmanuel","year":"1994","unstructured":"Corrada-Emmanuel, A.: Exact solution for superfluid film vortices on a torus. Phys. Rev. Lett. 72, 681\u2013684 (1994). \n                    https:\/\/doi.org\/10.1103\/PhysRevLett.72.681","journal-title":"Phys. Rev. Lett."},{"key":"9440_CR3","doi-asserted-by":"publisher","first-page":"2477","DOI":"10.1098\/rspa.2005.1492","volume":"461","author":"D Crowdy","year":"2005","unstructured":"Crowdy, D., Marshall, J.: Analytic formulae for the Kirchhoff\u2013Routh path function in multiply connected domains. Proc. R. Soc. A 461, 2477\u20132501 (2005)","journal-title":"Proc. R. Soc. A"},{"key":"9440_CR4","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1017\/S0022112085002324","volume":"358","author":"DG Dritschel","year":"1985","unstructured":"Dritschel, D.G.: The stability and energetics of co-rotating uniform vortices. J. Fluid Mech. 358, 95\u2013134 (1985)","journal-title":"J. Fluid Mech."},{"key":"9440_CR5","doi-asserted-by":"publisher","first-page":"20140890","DOI":"10.1098\/rspa.2014.0890","volume":"471","author":"DG Dritschel","year":"2016","unstructured":"Dritschel, D.G., Boatto, S.: The motion of point vortices on closed surfaces. Proc. R. Soc. A 471, 20140890 (2016). \n                    https:\/\/doi.org\/10.1098\/rspa.2014.0890","journal-title":"Proc. R. Soc. A"},{"key":"9440_CR6","doi-asserted-by":"publisher","first-page":"20120479","DOI":"10.1098\/rspa.2012.0479","volume":"469","author":"CC Green","year":"2012","unstructured":"Green, C.C., Marshall, J.S.: Green\u2019s function for the Laplace\u2013Beltrami operator on a toroidal surface. Proc. R. Soc. A 469, 20120479 (2012). \n                    https:\/\/doi.org\/10.1098\/rspa.2012.0479","journal-title":"Proc. R. Soc. A"},{"key":"9440_CR7","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1063\/1.524322","volume":"21","author":"D Hally","year":"1980","unstructured":"Hally, D.: Stability of streets of vortices on surfaces of revolution with a reflection symmetry. J. Math. Phys. 21, 211\u2013217 (1980). \n                    https:\/\/doi.org\/10.1137\/140971798","journal-title":"J. Math. Phys."},{"key":"9440_CR8","doi-asserted-by":"publisher","first-page":"063101","DOI":"10.1063\/1.4811454","volume":"54","author":"S Hwang","year":"2013","unstructured":"Hwang, S., Kim, S.-C.: Relative equilibria of point vortices on the hyperbolic sphere. J. Math. Phys. 54, 063101 (2013). \n                    https:\/\/doi.org\/10.1063\/1.4811454","journal-title":"J. Math. Phys."},{"key":"9440_CR9","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1017\/S0022112005003976","volume":"531","author":"ER Johnson","year":"2005","unstructured":"Johnson, E.R., McDonald, N.R.: Vortices near barriers with multiple gaps. J. Fluid Mech. 531, 335\u2013358 (2005). \n                    https:\/\/doi.org\/10.1017\/S0022112005003976","journal-title":"J. Fluid Mech."},{"key":"9440_CR10","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1098\/rspa.1999.0311","volume":"455","author":"Y Kimura","year":"1999","unstructured":"Kimura, Y.: Vortex motion on surfaces with constant curvature. Proc. R. Soc. A 455, 245\u2013259 (1999). \n                    https:\/\/doi.org\/10.1098\/rspa.1999.0311","journal-title":"Proc. R. Soc. A"},{"key":"9440_CR11","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1073\/pnas.27.12.570","volume":"27","author":"CC Lin","year":"1941","unstructured":"Lin, C.C.: On the motion of vortices in two-dimensions. I. Existence of the Kirchhoff-Routh function. Proc. Natl. Acad. Sci. 27, 570\u2013575 (1941a)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"9440_CR12","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1073\/pnas.27.12.575","volume":"27","author":"CC Lin","year":"1941","unstructured":"Lin, C.C.: On the motion of vortices in two-dimensions. II. Some further investigations on the Kirchhoff-Routh function. Proc. Natl. Acad. Sci. 27, 575\u2013577 (1941b)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"9440_CR13","volume-title":"Hydrodynamics","author":"H Lamb","year":"1932","unstructured":"Lamb, H.: Hydrodynamics, 6th edn. Cambridge University Press, Cambridge (1932)","edition":"6"},{"key":"9440_CR14","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1137\/S1111111102415569","volume":"2","author":"J Montaldi","year":"2003","unstructured":"Montaldi, J., Souli\u00e9re, A., Tokieda, T.: Vortex dynamics on a cylinder. SIAM J. Appl. Dyn. Syst. 2, 417\u2013430 (2003)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"9440_CR15","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/s13160-015-0168-6","volume":"32","author":"MS Nasser","year":"2015","unstructured":"Nasser, M.S., Sakajo, T., Murid, A.H., Wei, L.K.: A fast computational method for potential flows in multiply connected coastal domains. Jpn J. Ind. Appl. Math. 32, 205\u2013236 (2015)","journal-title":"Jpn J. Ind. Appl. Math."},{"key":"9440_CR16","doi-asserted-by":"publisher","first-page":"06142","DOI":"10.1088\/0169-5983\/46\/6\/061410","volume":"46","author":"R Nelson","year":"2014","unstructured":"Nelson, R., Sakajo, T.: Trapped vortices in multiply connected domains. Fluid Dyn. Des. 46, 06142 (2014). \n                    https:\/\/doi.org\/10.1088\/0169-5983\/46\/6\/061410","journal-title":"Fluid Dyn. Des."},{"key":"9440_CR17","volume-title":"The $$N$$-Vortex Problem, Analytic Techniques (Appl. Math. Sci)","author":"PK Newton","year":"2001","unstructured":"Newton, P.K.: The $$N$$-Vortex Problem, Analytic Techniques (Appl. Math. Sci), vol. 145. Springer, New York (2001)"},{"key":"9440_CR18","first-page":"771","volume":"22","author":"J Nycander","year":"1996","unstructured":"Nycander, J.: Analogy between the drift of planetary vortices and the precession of a spinning body. Plasma Phys. Rep. 22, 771\u2013774 (1996)","journal-title":"Plasma Phys. Rep."},{"key":"9440_CR19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511624063","volume-title":"Vortex Dynamics","author":"PG Saffman","year":"1993","unstructured":"Saffman, P.G.: Vortex Dynamics. Cambridge University Press, Cambridge (1993)"},{"key":"9440_CR20","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.physd.2004.05.009","volume":"196","author":"T Sakajo","year":"2004","unstructured":"Sakajo, T.: Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices. Phys. D 196, 243\u2013264 (2004)","journal-title":"Phys. D"},{"key":"9440_CR21","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.physd.2006.10.013","volume":"225","author":"T Sakajo","year":"2007","unstructured":"Sakajo, T.: Invariant dynamical systems embedded in the $$N$$-vortex problem on a sphere with pole vortices. Physica D, 217, (2006), pp. 142\u2013152. Phys. D 225, 235\u2013236 (2007). (erratum)","journal-title":"Phys. D"},{"key":"9440_CR22","doi-asserted-by":"publisher","first-page":"2589","DOI":"10.1098\/rspa.2009.0070","volume":"465","author":"T Sakajo","year":"2009","unstructured":"Sakajo, T.: Equation of motion for point vortices in multiply connected circular domains. Proc. R. Soc. A 465, 2589\u20132611 (2009). \n                    https:\/\/doi.org\/10.1098\/rspa.2009.0070","journal-title":"Proc. R. Soc. A"},{"key":"9440_CR23","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1007\/s00332-008-9019-9","volume":"18","author":"T Sakajo","year":"2008","unstructured":"Sakajo, T., Yagasaki, K.: Chaotic motion of the N-vortex problem on a sphere\u2014I. Saddle-centers in two-degree-of-freedom Hamiltonians. J. Nonlinear Sci. 18, 485\u2013525 (2008a)","journal-title":"J. Nonlinear Sci."},{"key":"9440_CR24","doi-asserted-by":"publisher","first-page":"2078","DOI":"10.1016\/j.physd.2008.02.001","volume":"237","author":"T Sakajo","year":"2008","unstructured":"Sakajo, T., Yagasaki, K.: Chaotic motion of the N-vortex problem on a sphere\u2014II. Saddle centers in three-degree-of-freedom Hamiltonians. Phys. D 237, 2078\u20132083 (2008b)","journal-title":"Phys. D"},{"key":"9440_CR25","doi-asserted-by":"publisher","first-page":"20160271","DOI":"10.1098\/rspa.2016.0271","volume":"472","author":"T Sakajo","year":"2016","unstructured":"Sakajo, T., Shimizu, Y.: Point vortex interactions on a toroidal surface. Proc. R. Soc. A 472, 20160271 (2016)","journal-title":"Proc. R. Soc. A"},{"key":"9440_CR26","unstructured":"Thomsom, J.J.: A Treatise on the Motion of Vortex Rings. An essay to which the Adams prize was adjudged in 1882, in the University of Cambridge, Macmillan, London (1883)"},{"key":"9440_CR27","first-page":"1573","volume":"23","author":"VK Tkachenko","year":"1966","unstructured":"Tkachenko, V.K.: Stability of vortex lattices Sov. Phys. JETS 23, 1573\u20131585 (1966)","journal-title":"Phys. JETS"},{"key":"9440_CR28","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1103\/RevModPhys.82.1301","volume":"82","author":"AM Turner","year":"2010","unstructured":"Turner, A.M., Vitelli, V., Nelson, D.R.: Vortices on curved surfaces. Rev. Mod. Phys. 82, 1301\u20131348 (2010). \n                    https:\/\/doi.org\/10.1103\/RevModPhys.82.1301","journal-title":"Rev. Mod. Phys."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-017-9440-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-017-9440-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-017-9440-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T06:03:50Z","timestamp":1589695430000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-017-9440-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,4]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["9440"],"URL":"https:\/\/doi.org\/10.1007\/s00332-017-9440-z","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"type":"print","value":"0938-8974"},{"type":"electronic","value":"1432-1467"}],"subject":[],"published":{"date-parts":[[2018,1,4]]},"assertion":[{"value":"10 April 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}