{"id":"https://openalex.org/W2981080173","doi":"https://doi.org/10.1090/mcom/3592","title":"On the second Lyapunov exponent of some multidimensional continued fraction algorithms","display_name":"On the second Lyapunov exponent of some multidimensional continued fraction algorithms","publication_year":2020,"publication_date":"2020-09-09","ids":{"openalex":"https://openalex.org/W2981080173","doi":"https://doi.org/10.1090/mcom/3592","mag":"2981080173"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3592","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3592","pdf_url":"https://www.ams.org/mcom/2021-90-328/S0025-5718-2020-03592-3/S0025-5718-2020-03592-3.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","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2021-90-328/S0025-5718-2020-03592-3/S0025-5718-2020-03592-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079296049","display_name":"Val\u00e9rie Berth\u00e9","orcid":"https://orcid.org/0000-0001-5561-7882"},"institutions":[{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Val\u00e9rie Berth\u00e9","raw_affiliation_strings":["Institut de Recherche en Informatique Fondamentale"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Informatique Fondamentale","institution_ids":["https://openalex.org/I4210117673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079044708","display_name":"Wolfgang Steiner","orcid":"https://orcid.org/0000-0002-6035-6856"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Wolfgang Steiner","raw_affiliation_strings":["Universit\u00c3\u00a9 de Paris, IRIF, CNRS, F\u00e2\u0080\u009375006 Paris, France","Institut de Recherche en Informatique Fondamentale"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00c3\u00a9 de Paris, IRIF, CNRS, F\u00e2\u0080\u009375006 Paris, France","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Institut de Recherche en Informatique Fondamentale","institution_ids":["https://openalex.org/I4210117673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020243260","display_name":"J\u00f6rg \u039c. Thuswaldner","orcid":"https://orcid.org/0000-0001-5308-762X"},"institutions":[{"id":"https://openalex.org/I182712176","display_name":"Montanuniversit\u00e4t Leoben","ror":"https://ror.org/02fhfw393","country_code":"AT","type":"education","lineage":["https://openalex.org/I182712176"]},{"id":"https://openalex.org/I4210135925","display_name":"Materials Center Leoben (Austria)","ror":"https://ror.org/04s620254","country_code":"AT","type":"company","lineage":["https://openalex.org/I4210135925"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"J\u00f6rg M. Thuswaldner","raw_affiliation_strings":["Chair of Mathematics and Statistics, University of Leoben, A\u00e2\u0080\u00938700 Leoben, Austria","Chair of Mathematics and Statistics, University of Leoben, A-8700 Leoben, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Mathematics and Statistics, University of Leoben, A\u00e2\u0080\u00938700 Leoben, Austria","institution_ids":["https://openalex.org/I182712176","https://openalex.org/I4210135925"]},{"raw_affiliation_string":"Chair of Mathematics and Statistics, University of Leoben, A-8700 Leoben, Austria","institution_ids":["https://openalex.org/I182712176"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0737249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"90","issue":"328","first_page":"883","last_page":"905"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.7597000002861023,"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":0.7597000002861023,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.048900000751018524,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.03440000116825104,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.8240371346473694},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.609375},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.49067509174346924},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45824453234672546},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43954694271087646},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3488359749317169},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28739404678344727},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1136370301246643},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.03443148732185364}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.8240371346473694},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.609375},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.49067509174346924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45824453234672546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43954694271087646},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3488359749317169},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28739404678344727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1136370301246643},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.03443148732185364},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/mcom/3592","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3592","pdf_url":"https://www.ams.org/mcom/2021-90-328/S0025-5718-2020-03592-3/S0025-5718-2020-03592-3.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:1910.09386","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.09386","pdf_url":"https://arxiv.org/pdf/1910.09386","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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-02320903v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02320903","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.archives-ouvertes.fr/hal-02320903","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-02320903v2","is_oa":true,"landing_page_url":"https://hal.science/hal-02320903","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0025-5718","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1910.09386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1910.09386","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1090/mcom/3592","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3592","pdf_url":"https://www.ams.org/mcom/2021-90-328/S0025-5718-2020-03592-3/S0025-5718-2020-03592-3.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":[],"awards":[{"id":"https://openalex.org/G1893710830","display_name":"Fractals and Words: Topological, Dynamical, and Combinatorial Aspects","funder_award_id":"P27050","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3142032254","display_name":null,"funder_award_id":"P29910","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4127002148","display_name":null,"funder_award_id":"ANR- 18-CE40-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4166017908","display_name":null,"funder_award_id":"ANR- 18-CE40-0007","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4167063056","display_name":null,"funder_award_id":"P27050","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4340448372","display_name":"Dynamics, geometry, and arithmetic of Numeration","funder_award_id":"P29910","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5917783284","display_name":"Geometry of Numbers and Diophantine Approximation","funder_award_id":"I3466","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7536767931","display_name":"Computer orbits for Discrete Dynamical Systems","funder_award_id":"ANR-18-CE40-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7771306536","display_name":null,"funder_award_id":"ANR-18-CE40-0007","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8706860382","display_name":null,"funder_award_id":"I3466","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W560925849","https://openalex.org/W584208200","https://openalex.org/W623586698","https://openalex.org/W1500762505","https://openalex.org/W1973422585","https://openalex.org/W1975710829","https://openalex.org/W1982493292","https://openalex.org/W1996121512","https://openalex.org/W1998694370","https://openalex.org/W2022761334","https://openalex.org/W2025308004","https://openalex.org/W2026654212","https://openalex.org/W2035892308","https://openalex.org/W2048037412","https://openalex.org/W2076032753","https://openalex.org/W2082996901","https://openalex.org/W2115906782","https://openalex.org/W2121422613","https://openalex.org/W2138091643","https://openalex.org/W2163620018","https://openalex.org/W2167766124","https://openalex.org/W2168567490","https://openalex.org/W2169004268","https://openalex.org/W2172605325","https://openalex.org/W2230778605","https://openalex.org/W2316412685","https://openalex.org/W2324299322","https://openalex.org/W2735466101","https://openalex.org/W2943383440","https://openalex.org/W3121286321"],"related_works":["https://openalex.org/W3170596679","https://openalex.org/W2030128136","https://openalex.org/W2000983461","https://openalex.org/W2315492480","https://openalex.org/W2008992764","https://openalex.org/W2981080173","https://openalex.org/W4213396896","https://openalex.org/W4214784561","https://openalex.org/W4214959400","https://openalex.org/W4213464843"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,14,22,72],"strong":[3],"convergence":[4],"of":[5,26,83],"certain":[6],"multidimensional":[7,54],"continued":[8,45,55],"fraction":[9,46,56],"algorithms.":[10,47],"In":[11],"particular,":[12],"in":[13],"two-":[15],"and":[16,31],"three-dimensional":[17],"case,":[18],"we":[19,38],"prove":[20],"that":[21,51],"second":[23],"Lyapunov":[24],"exponent":[25],"Selmer\u00e2\u0080\u0099s":[27],"algorithm":[28,74],"is":[29,77],"negative":[30],"bound":[32],"it":[33],"away":[34],"from":[35],"zero.":[36,85],"Moreover,":[37],"give":[39],"heuristic":[40],"results":[41,49],"on":[42,80],"several":[43],"other":[44],"Our":[48],"indicate":[50],"all":[52],"classical":[53],"algorithms":[57],"cease":[58],"to":[59,70],"be":[60,71],"strongly":[61],"convergent":[62],"for":[63],"high":[64],"dimensions.":[65],"The":[66],"only":[67,79],"exception":[68],"seems":[69],"Arnoux\u00e2\u0080\u0093Rauzy":[73],"which,":[75],"however,":[76],"defined":[78],"a":[81],"set":[82],"measure":[84]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2019-10-25T00:00:00"}
