{"id":"https://openalex.org/W2951600536","doi":"https://doi.org/10.48550/arxiv.1401.5866","title":"Farey map, Diophantine approximation and Bruhat-Tits tree","display_name":"Farey map, Diophantine approximation and Bruhat-Tits tree","publication_year":2014,"publication_date":"2014-01-23","ids":{"openalex":"https://openalex.org/W2951600536","doi":"https://doi.org/10.48550/arxiv.1401.5866","mag":"2951600536"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1401.5866","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.5866","pdf_url":"https://arxiv.org/pdf/1401.5866","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1401.5866","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100616112","display_name":"Dong Han Kim","orcid":"https://orcid.org/0000-0001-5764-9466","observed_orcids":["https://orcid.org/0000-0001-5764-9466"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Dong Han","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016495222","display_name":"Seonhee Lim","orcid":"https://orcid.org/0000-0002-7189-3155","observed_orcids":["https://orcid.org/0000-0002-7189-3155"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lim, Seonhee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102816462","display_name":"Hitoshi Nakada","orcid":"https://orcid.org/0000-0001-9966-8593","observed_orcids":["https://orcid.org/0000-0001-9966-8593"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nakada, Hitoshi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028181901","display_name":"Rie Natsui","orcid":"https://orcid.org/0000-0001-5078-8826","observed_orcids":["https://orcid.org/0000-0001-5078-8826"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Natsui, Rie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13234","display_name":"advanced mathematical theories","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11166","display_name":"Analytic Number Theory Research","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/farey-map","display_name":"Farey map","score":0.9670000076293945},{"id":"https://openalex.org/keywords/diophantine-approximation","display_name":"Diophantine approximation","score":0.9259999990463257},{"id":"https://openalex.org/keywords/gauss-map","display_name":"Gauss map","score":0.8379999995231628},{"id":"https://openalex.org/keywords/bruhat-tits-tree","display_name":"Bruhat-Tits tree","score":0.8740000128746033},{"id":"https://openalex.org/keywords/geodesic-flow","display_name":"geodesic flow","score":0.9089999794960022},{"id":"https://openalex.org/keywords/ergodic-measures","display_name":"ergodic measures","score":0.9639999866485596},{"id":"https://openalex.org/keywords/arithmetic-dynamics","display_name":"arithmetic dynamics","score":0.30399999022483826}],"concepts":[{"id":"https://openalex.org/C93157843","wikidata":"https://www.wikidata.org/wiki/Q1396592","display_name":"Farey sequence","level":2,"score":0.9047878980636597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6941164135932922},{"id":"https://openalex.org/C2776441312","wikidata":"https://www.wikidata.org/wiki/Q575710","display_name":"Gauss map","level":2,"score":0.596514880657196},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5504077076911926},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.49747422337532043},{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.48499318957328796},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.48322567343711853},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4751672148704529},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.44034868478775024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3464195132255554},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33677610754966736},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2632644772529602},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1681191623210907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11811289191246033},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.06774917244911194},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1401.5866","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.5866","pdf_url":"https://arxiv.org/pdf/1401.5866","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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:CiteSeerX.psu:10.1.1.753.4922","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.753.4922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1401.5866.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1401.5866","doi":"https://doi.org/10.48550/arxiv.1401.5866","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1401.5866","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1401.5866","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.5866","pdf_url":"https://arxiv.org/pdf/1401.5866","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W252156777","https://openalex.org/W1575972212","https://openalex.org/W1671860181","https://openalex.org/W1974936994","https://openalex.org/W2004702567","https://openalex.org/W2080253405","https://openalex.org/W2331228503"],"related_works":["https://openalex.org/W2044767466","https://openalex.org/W3152652070","https://openalex.org/W3125557654","https://openalex.org/W2955173759","https://openalex.org/W4288288032","https://openalex.org/W2951600536","https://openalex.org/W2092042588","https://openalex.org/W2106189707","https://openalex.org/W4289784642","https://openalex.org/W2611889129"],"abstract_inverted_index":{"Based":[0],"on":[1,6],"Broise-Alamichel":[2],"and":[3,76],"Paulin's":[4],"work":[5],"the":[7,12,17,20,29,34,45,62,68,73,77],"Gauss":[8,21],"map":[9,22,43],"corresponding":[10],"to":[11,26],"principal":[13],"convergents,":[14],"we":[15,66],"continue":[16],"study":[18],"of":[19,44],"via":[23],"Farey":[24,36,52,74],"maps":[25,75],"contain":[27],"all":[28,61],"intermediate":[30,63],"convergents.":[31,64],"We":[32,48],"define":[33,50],"geometric":[35],"map,":[37],"which":[38,59],"is":[39],"given":[40],"by":[41],"time-1":[42],"geodesic":[46],"flow.":[47],"also":[49],"algebraic":[51],"maps,":[53],"better":[54],"suited":[55],"for":[56,72],"arithmetic":[57],"properties,":[58],"produce":[60],"Then":[65],"obtain":[67],"ergodic":[69],"invariant":[70],"measures":[71],"convergent":[78],"speed.":[79]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}