{"id":"https://openalex.org/W1509133757","doi":"https://doi.org/10.1090/mcom/3153","title":"A minimal-variable symplectic integrator on spheres","display_name":"A minimal-variable symplectic integrator on spheres","publication_year":2016,"publication_date":"2016-04-14","ids":{"openalex":"https://openalex.org/W1509133757","doi":"https://doi.org/10.1090/mcom/3153","mag":"1509133757"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3153","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3153","pdf_url":"https://www.ams.org/mcom/2017-86-307/S0025-5718-2016-03153-1/S0025-5718-2016-03153-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2017-86-307/S0025-5718-2016-03153-1/S0025-5718-2016-03153-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005515472","display_name":"Robert I. McLachlan","orcid":"https://orcid.org/0000-0003-0392-4957"},"institutions":[{"id":"https://openalex.org/I51158804","display_name":"Massey University","ror":"https://ror.org/052czxv31","country_code":"NZ","type":"education","lineage":["https://openalex.org/I51158804"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Robert McLachlan","raw_affiliation_strings":["Institute of Fundamental Sciences, Massey University, New Zealand","Institute of Fundamental Sciences, Massey University , New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Fundamental Sciences, Massey University, New Zealand","institution_ids":["https://openalex.org/I51158804"]},{"raw_affiliation_string":"Institute of Fundamental Sciences, Massey University , New Zealand","institution_ids":["https://openalex.org/I51158804"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052120629","display_name":"Klas Modin","orcid":"https://orcid.org/0000-0001-6900-1122"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Klas Modin","raw_affiliation_strings":["Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010971554","display_name":"Olivier Verdier","orcid":"https://orcid.org/0000-0003-3699-6244"},"institutions":[{"id":"https://openalex.org/I179863766","display_name":"Western Norway University of Applied Sciences","ror":"https://ror.org/05phns765","country_code":"NO","type":"education","lineage":["https://openalex.org/I179863766"]},{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Olivier Verdier","raw_affiliation_strings":["Department of Computing, Mathematics and Physics, Bergen University College, Norway","Department of Computing, Mathematics, and Physics, Bergen University College, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing, Mathematics and Physics, Bergen University College, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Department of Computing, Mathematics, and Physics, Bergen University College, Norway","institution_ids":["https://openalex.org/I179863766"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5032,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.93915017,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"86","issue":"307","first_page":"2325","last_page":"2344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8156839609146118},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.7235754728317261},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.6853508949279785},{"id":"https://openalex.org/keywords/symplectic-integrator","display_name":"Symplectic integrator","score":0.5697007179260254},{"id":"https://openalex.org/keywords/symplectic-vector-space","display_name":"Symplectic vector space","score":0.5518187880516052},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.5252832174301147},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.520811915397644},{"id":"https://openalex.org/keywords/cotangent-bundle","display_name":"Cotangent bundle","score":0.47156593203544617},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45651838183403015},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4504453241825104},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.44620388746261597},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.43103986978530884},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2973063588142395},{"id":"https://openalex.org/keywords/symplectic-representation","display_name":"Symplectic representation","score":0.2390451431274414},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.23015308380126953},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1934318244457245},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11818701028823853}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8156839609146118},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7235754728317261},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6853508949279785},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.5697007179260254},{"id":"https://openalex.org/C125849494","wikidata":"https://www.wikidata.org/wiki/Q766774","display_name":"Symplectic vector space","level":5,"score":0.5518187880516052},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.5252832174301147},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.520811915397644},{"id":"https://openalex.org/C7979169","wikidata":"https://www.wikidata.org/wiki/Q1142143","display_name":"Cotangent bundle","level":3,"score":0.47156593203544617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45651838183403015},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4504453241825104},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.44620388746261597},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.43103986978530884},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2973063588142395},{"id":"https://openalex.org/C104586451","wikidata":"https://www.wikidata.org/wiki/Q771008","display_name":"Symplectic representation","level":4,"score":0.2390451431274414},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.23015308380126953},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1934318244457245},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11818701028823853},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/mcom/3153","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3153","pdf_url":"https://www.ams.org/mcom/2017-86-307/S0025-5718-2016-03153-1/S0025-5718-2016-03153-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1402.3334","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1402.3334","pdf_url":"https://arxiv.org/pdf/1402.3334","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:publications.lib.chalmers.se:247145","is_oa":false,"landing_page_url":"http://publications.lib.chalmers.se/publication/247145-a-minimal-variable-symplectic-integrator-on-spheres","pdf_url":null,"source":{"id":"https://openalex.org/S4377196470","display_name":"Chalmers Publication Library (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text.Article.Journal.PeerReviewed"},{"id":"pmh:oai:research.chalmers.se:230385","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/230385","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:research.chalmers.se:247145","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/e4c3c89c-2d5e-40b9-a617-507f3337b2de","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"doi:10.1090/mcom/3153","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3153","pdf_url":"https://www.ams.org/mcom/2017-86-307/S0025-5718-2016-03153-1/S0025-5718-2016-03153-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.550000011920929}],"awards":[{"id":"https://openalex.org/G1064336709","display_name":null,"funder_award_id":"2014-5823","funder_id":"https://openalex.org/F4320324135","funder_display_name":"Kempestiftelserna"},{"id":"https://openalex.org/G1460875345","display_name":null,"funder_award_id":"2014-5823","funder_id":"https://openalex.org/F4320320939","funder_display_name":"Swedish Foundation for International Cooperation in Research and Higher Education"},{"id":"https://openalex.org/G1484560145","display_name":null,"funder_award_id":"SMK-1238","funder_id":"https://openalex.org/F4320320940","funder_display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning"},{"id":"https://openalex.org/G215244912","display_name":null,"funder_award_id":"ICA12-0052","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2576552314","display_name":"Numeriska metoder f\u00f6r ber\u00e4kningsanatomi","funder_award_id":"ICA12-0052","funder_id":"https://openalex.org/F4320320940","funder_display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning"},{"id":"https://openalex.org/G2933274832","display_name":null,"funder_award_id":"SMK-1238","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3356652419","display_name":"Geometry and Computational Anatomy","funder_award_id":"661482","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G417026515","display_name":null,"funder_award_id":"661482","funder_id":"https://openalex.org/F4320324135","funder_display_name":"Kempestiftelserna"},{"id":"https://openalex.org/G4723844241","display_name":null,"funder_award_id":"661482","funder_id":"https://openalex.org/F4320320940","funder_display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning"},{"id":"https://openalex.org/G541159123","display_name":null,"funder_award_id":"2014-5823","funder_id":"https://openalex.org/F4320320940","funder_display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning"},{"id":"https://openalex.org/G5540993094","display_name":null,"funder_award_id":"SMK-1238","funder_id":"https://openalex.org/F4320320939","funder_display_name":"Swedish Foundation for International Cooperation in Research and Higher Education"},{"id":"https://openalex.org/G5700451009","display_name":null,"funder_award_id":"661482","funder_id":"https://openalex.org/F4320320939","funder_display_name":"Swedish Foundation for International Cooperation in Research and Higher Education"},{"id":"https://openalex.org/G5956553722","display_name":null,"funder_award_id":"SMK-1238","funder_id":"https://openalex.org/F4320324135","funder_display_name":"Kempestiftelserna"},{"id":"https://openalex.org/G7309302117","display_name":null,"funder_award_id":"ICA12-0052","funder_id":"https://openalex.org/F4320324135","funder_display_name":"Kempestiftelserna"},{"id":"https://openalex.org/G7317358388","display_name":null,"funder_award_id":"2014-5823","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8466614354","display_name":null,"funder_award_id":"ICA12-0052","funder_id":"https://openalex.org/F4320320939","funder_display_name":"Swedish Foundation for International Cooperation in Research and Higher Education"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320939","display_name":"Swedish Foundation for International Cooperation in Research and Higher Education","ror":"https://ror.org/0561xc723"},{"id":"https://openalex.org/F4320320940","display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning","ror":"https://ror.org/044wr7g58"},{"id":"https://openalex.org/F4320324135","display_name":"Kempestiftelserna","ror":"https://ror.org/05cszw148"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1509133757.pdf","grobid_xml":"https://content.openalex.org/works/W1509133757.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W1495727713","https://openalex.org/W1498452679","https://openalex.org/W1516474119","https://openalex.org/W1524590822","https://openalex.org/W1544770838","https://openalex.org/W1588860486","https://openalex.org/W1648694285","https://openalex.org/W1978652497","https://openalex.org/W1979251648","https://openalex.org/W1996016656","https://openalex.org/W1997105074","https://openalex.org/W2003161517","https://openalex.org/W2006042718","https://openalex.org/W2018407306","https://openalex.org/W2020700123","https://openalex.org/W2025706093","https://openalex.org/W2030211848","https://openalex.org/W2031014249","https://openalex.org/W2041678031","https://openalex.org/W2044078245","https://openalex.org/W2059469074","https://openalex.org/W2059552911","https://openalex.org/W2068183683","https://openalex.org/W2069185213","https://openalex.org/W2076542052","https://openalex.org/W2078564496","https://openalex.org/W2083247933","https://openalex.org/W2083623028","https://openalex.org/W2084057209","https://openalex.org/W2091903312","https://openalex.org/W2098550758","https://openalex.org/W2111027538","https://openalex.org/W2120781947","https://openalex.org/W2139968887","https://openalex.org/W2156332739","https://openalex.org/W2158168151","https://openalex.org/W2502666551","https://openalex.org/W2886665676","https://openalex.org/W2947056241","https://openalex.org/W2969232873","https://openalex.org/W2970323723","https://openalex.org/W3040096869","https://openalex.org/W3098849882","https://openalex.org/W3103654402","https://openalex.org/W3103748505","https://openalex.org/W4242802548","https://openalex.org/W6637125287"],"related_works":["https://openalex.org/W2045132191","https://openalex.org/W3203336796","https://openalex.org/W3106386282","https://openalex.org/W4247519482","https://openalex.org/W2953049006","https://openalex.org/W4300511880","https://openalex.org/W3099607900","https://openalex.org/W2949644599","https://openalex.org/W1969998195","https://openalex.org/W2647145184"],"abstract_inverted_index":{"We":[0],"construct":[1],"a":[2,33,41,61,65],"symplectic,":[3],"globally":[4],"defined,":[5],"minimal-variable,":[6],"equivariant":[7],"integrator":[8,53,86],"on":[9,32],"products":[10],"of":[11,14,29,44,50,84],"2-spheres.":[12],"Examples":[13],"corresponding":[15],"Hamiltonian":[16],"systems,":[17,20],"called":[18],"spin":[19,39],"include":[21],"the":[22,27,36,45,57,82,85,92,97],"reduced":[23],"free":[24],"rigid":[25],"body,":[26],"motion":[28],"point":[30],"vortices":[31],"sphere,":[34],"and":[35,73,90],"classical":[37],"Heisenberg":[38],"chain,":[40],"spatial":[42],"discretisation":[43],"Landau\u2013Lifshitz":[46],"equation.":[47],"The":[48],"existence":[49],"such":[51],"an":[52],"is":[54,59,77,87,99],"remarkable,":[55],"as":[56],"sphere":[58],"neither":[60],"vector":[62],"space,":[63],"nor":[64],"cotangent":[66],"bundle,":[67],"has":[68],"no":[69],"global":[70],"coordinate":[71],"chart,":[72],"its":[74],"symplectic":[75],"form":[76],"not":[78],"even":[79],"exact.":[80],"Moreover,":[81],"formulation":[83],"very":[88],"simple,":[89],"resembles":[91],"geodesic":[93],"midpoint":[94],"method,":[95],"although":[96],"latter":[98],"<italic>not</italic>":[100],"symplectic.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}
