{"id":"https://openalex.org/W3104623519","doi":"https://doi.org/10.1112/jlms/jdw020","title":"Geometry of an elliptic difference equation related to Q4","display_name":"Geometry of an elliptic difference equation related to Q4","publication_year":2016,"publication_date":"2016-04-28","ids":{"openalex":"https://openalex.org/W3104623519","doi":"https://doi.org/10.1112/jlms/jdw020","mag":"3104623519"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdw020","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdw020","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1506.04457","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068680675","display_name":"James Atkinson","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"James Atkinson","raw_affiliation_strings":["4 Fetcham Court, Newcastle upon Tyne, NE3 2U, United Kingdom"],"affiliations":[{"raw_affiliation_string":"4 Fetcham Court, Newcastle upon Tyne, NE3 2U, United Kingdom","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059966100","display_name":"Phil Howes","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Phil Howes","raw_affiliation_strings":["c/o School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW 2006, Australia, howespt@gmail.com, nalini.joshi@sydney.edu.au","c/o School of Mathematics and Statistics F07The University of SydneySydney, NSW 2006Australiahowespt@gmail.comnalini.joshi@sydney.edu.au"],"affiliations":[{"raw_affiliation_string":"c/o School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW 2006, Australia, howespt@gmail.com, nalini.joshi@sydney.edu.au","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"c/o School of Mathematics and Statistics F07The University of SydneySydney, NSW 2006Australiahowespt@gmail.comnalini.joshi@sydney.edu.au","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087875378","display_name":"Nalini Joshi","orcid":"https://orcid.org/0000-0001-7504-4444"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Nalini Joshi","raw_affiliation_strings":["c/o School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW 2006, Australia, howespt@gmail.com, nalini.joshi@sydney.edu.au","c/o School of Mathematics and Statistics F07The University of SydneySydney, NSW 2006Australiahowespt@gmail.comnalini.joshi@sydney.edu.au"],"affiliations":[{"raw_affiliation_string":"c/o School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW 2006, Australia, howespt@gmail.com, nalini.joshi@sydney.edu.au","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"c/o School of Mathematics and Statistics F07The University of SydneySydney, NSW 2006Australiahowespt@gmail.comnalini.joshi@sydney.edu.au","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012748195","display_name":"Nobutaka Nakazono","orcid":"https://orcid.org/0000-0003-4608-285X"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Nobutaka Nakazono","raw_affiliation_strings":["c/o School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW 2006, Australia, howespt@gmail.com, nalini.joshi@sydney.edu.au","c/o School of Mathematics and Statistics F07The University of SydneySydney, NSW 2006Australiahowespt@gmail.comnalini.joshi@sydney.edu.au"],"affiliations":[{"raw_affiliation_string":"c/o School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW 2006, Australia, howespt@gmail.com, nalini.joshi@sydney.edu.au","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"c/o School of Mathematics and Statistics F07The University of SydneySydney, NSW 2006Australiahowespt@gmail.comnalini.joshi@sydney.edu.au","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5068680675"],"corresponding_institution_ids":[],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":1.8056,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.86535868,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"93","issue":"3","first_page":"763","last_page":"784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.8352625370025635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.731683611869812},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6294071674346924},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5921887755393982},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5185173749923706},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.4789900481700897},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.4625956118106842},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.44817909598350525},{"id":"https://openalex.org/keywords/novikov-self-consistency-principle","display_name":"Novikov self-consistency principle","score":0.44802412390708923},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4415154457092285},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4390198290348053},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4307582974433899},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4231686592102051},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39767134189605713},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27376317977905273},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1331239640712738},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08239024877548218},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0653601586818695}],"concepts":[{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.8352625370025635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.731683611869812},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6294071674346924},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5921887755393982},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5185173749923706},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.4789900481700897},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.4625956118106842},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.44817909598350525},{"id":"https://openalex.org/C114170632","wikidata":"https://www.wikidata.org/wiki/Q2003641","display_name":"Novikov self-consistency principle","level":2,"score":0.44802412390708923},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4415154457092285},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4390198290348053},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4307582974433899},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4231686592102051},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39767134189605713},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27376317977905273},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1331239640712738},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08239024877548218},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0653601586818695},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1112/jlms/jdw020","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdw020","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1506.04457","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.04457","pdf_url":"https://arxiv.org/pdf/1506.04457","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:open-archive.highwire.org:jlms:93/3/763","is_oa":false,"landing_page_url":"http://jlms.oxfordjournals.org/cgi/content/short/93/3/763","pdf_url":null,"source":{"id":"https://openalex.org/S4406923041","display_name":"HighWire Press Open Archive","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1506.04457","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.04457","pdf_url":"https://arxiv.org/pdf/1506.04457","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1480944724","https://openalex.org/W1599288848","https://openalex.org/W1642629289","https://openalex.org/W1677083650","https://openalex.org/W1714496566","https://openalex.org/W1929275016","https://openalex.org/W1965897591","https://openalex.org/W1976677460","https://openalex.org/W1983434079","https://openalex.org/W1986569583","https://openalex.org/W2011656937","https://openalex.org/W2011934178","https://openalex.org/W2016923340","https://openalex.org/W2061985873","https://openalex.org/W2065828382","https://openalex.org/W2089044087","https://openalex.org/W2096668210","https://openalex.org/W2105962016","https://openalex.org/W2122281309","https://openalex.org/W2212380868","https://openalex.org/W2267296100","https://openalex.org/W2952734730","https://openalex.org/W2963439835","https://openalex.org/W3037659403","https://openalex.org/W3098067714","https://openalex.org/W3098592340","https://openalex.org/W3100414330","https://openalex.org/W3104561840","https://openalex.org/W3105824894","https://openalex.org/W3106098181","https://openalex.org/W3106275102","https://openalex.org/W3146559140","https://openalex.org/W4239273885","https://openalex.org/W4248269519"],"related_works":["https://openalex.org/W1985910657","https://openalex.org/W420785306","https://openalex.org/W2229847015","https://openalex.org/W2949949163","https://openalex.org/W3100606162","https://openalex.org/W4302355000","https://openalex.org/W2091690678","https://openalex.org/W1980590680","https://openalex.org/W2297581160","https://openalex.org/W4307756502"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"investigate":[4],"a":[5,23,40,44,119,139],"nonlinear":[6],"non-autonomous":[7],"elliptic":[8,142],"difference":[9,143],"equation,":[10,30],"which":[11,117],"was":[12],"constructed":[13],"by":[14,19,112],"Ramani,":[15],"Carstea":[16],"and":[17,59,86],"Grammaticos":[18],"integrable":[20,141],"deautonomization":[21,104],"of":[22,26,71,110,131,138],"periodic":[24],"reduction":[25,120,130],"the":[27,68,72,103,108,124,132],"discrete":[28],"Krichever\u2013Novikov":[29],"or":[31],"Q4.":[32],"We":[33,100],"show":[34,101],"how":[35],"to":[36],"construct":[37],"it":[38,66],"as":[39],"birational":[41],"mapping":[42],"on":[43],"rational":[45],"surface":[46],"blown":[47],"up":[48],"at":[49],"eight":[50],"points":[51],"in":[52,67,123],"P":[53,56],"1":[54,57,84,96],"\u00d7":[55],",":[58],"find":[60],"its":[61,87],"affine":[62],"Weyl":[63],"symmetry,":[64],"placing":[65],"geometric":[69],"framework":[70],"Painlev\u00e9":[73],"equations.":[74],"The":[75],"initial":[76],"value":[77],"space":[78],"is":[79,90,105,118],"ell-":[80],"A":[81,127],"0":[82],"(":[83,92,95],")":[85,97,98],"symmetry":[88],"group":[89],"W":[91],"F":[93],"4":[94],".":[99],"that":[102],"consistent":[106],"with":[107],"lattice-geometry":[109],"Q4":[111,122],"giving":[113],"an":[114],"alternative":[115],"construction,":[116],"from":[121],"usual":[125],"sense.":[126],"more":[128],"symmetric":[129],"same":[133],"kind":[134],"provides":[135],"another":[136],"example":[137],"second-order":[140],"equation.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}