{"id":"https://openalex.org/W2024428978","doi":"https://doi.org/10.1017/s0960129507005981","title":"Discrete-time and continuous-time modelling: some bridges and gaps","display_name":"Discrete-time and continuous-time modelling: some bridges and gaps","publication_year":2007,"publication_date":"2007-04-01","ids":{"openalex":"https://openalex.org/W2024428978","doi":"https://doi.org/10.1017/s0960129507005981","mag":"2024428978"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129507005981","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129507005981","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077215850","display_name":"H. Krivine","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I4210097733","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques","ror":"https://ror.org/00w67e447","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097733"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"HUBERT KRIVINE","raw_affiliation_strings":["LPTMS, B\u00e2timent 100, Universit\u00e9 Paris-Sud, F-91405 Orsay Email:","Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LPTMS, B\u00e2timent 100, Universit\u00e9 Paris-Sud, F-91405 Orsay Email:","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques","institution_ids":["https://openalex.org/I4210097733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068924391","display_name":"Annick Lesne","orcid":"https://orcid.org/0000-0002-6647-612X"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210140797","display_name":"Laboratoire de Physique Th\u00e9orique de la Mati\u00e8re Condens\u00e9e","ror":"https://ror.org/04zaaa143","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210098836","https://openalex.org/I4210140797"]},{"id":"https://openalex.org/I84909340","display_name":"Institut des Hautes \u00c9tudes Scientifiques","ror":"https://ror.org/05d5m2r55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I84909340"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"ANNICK LESNE","raw_affiliation_strings":["Institut des Hautes \u00c9tudes Scientifiques, 35 route de Chartres, F-91440 Bures-sur-Yvette, France Email:","LPTMC UMR7600, Universit\u00e9 Pierre et Marie Curie-Paris 6, 4 place Jussieu, F-75252 Paris Email:","Laboratoire de Physique Th\u00e9orique de la Mati\u00e8re Condens\u00e9e","Institut des Hautes \u00c9tudes Scientifiques"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut des Hautes \u00c9tudes Scientifiques, 35 route de Chartres, F-91440 Bures-sur-Yvette, France Email:","institution_ids":["https://openalex.org/I84909340"]},{"raw_affiliation_string":"LPTMC UMR7600, Universit\u00e9 Pierre et Marie Curie-Paris 6, 4 place Jussieu, F-75252 Paris Email:","institution_ids":["https://openalex.org/I39804081"]},{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique de la Mati\u00e8re Condens\u00e9e","institution_ids":["https://openalex.org/I4210140797"]},{"raw_affiliation_string":"Institut des Hautes \u00c9tudes Scientifiques","institution_ids":["https://openalex.org/I84909340"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045332029","display_name":"Jacques Treiner","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I4210097733","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques","ror":"https://ror.org/00w67e447","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097733"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"JACQUES TREINER","raw_affiliation_strings":["LPTMS, B\u00e2timent 100, Universit\u00e9 Paris-Sud, F-91405 Orsay Email:","Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LPTMS, B\u00e2timent 100, Universit\u00e9 Paris-Sud, F-91405 Orsay Email:","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques","institution_ids":["https://openalex.org/I4210097733"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077215850"],"corresponding_institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210097733"],"apc_list":null,"apc_paid":null,"fwci":1.017,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.75899113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"17","issue":"2","first_page":"261","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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":0.9979000091552734,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9976999759674072,"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/discretization","display_name":"Discretization","score":0.678399384021759},{"id":"https://openalex.org/keywords/continuous-modelling","display_name":"Continuous modelling","score":0.6583359837532043},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.6185788512229919},{"id":"https://openalex.org/keywords/discrete-modelling","display_name":"Discrete modelling","score":0.513934314250946},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5046964883804321},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49894118309020996},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4880343973636627},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.47836726903915405},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3920958638191223},{"id":"https://openalex.org/keywords/discrete-system","display_name":"Discrete system","score":0.3369026482105255},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24422144889831543},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1823389232158661},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07549440860748291}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.678399384021759},{"id":"https://openalex.org/C10184394","wikidata":"https://www.wikidata.org/wiki/Q5165491","display_name":"Continuous modelling","level":2,"score":0.6583359837532043},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.6185788512229919},{"id":"https://openalex.org/C81146285","wikidata":"https://www.wikidata.org/wiki/Q5282053","display_name":"Discrete modelling","level":3,"score":0.513934314250946},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5046964883804321},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49894118309020996},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4880343973636627},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.47836726903915405},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3920958638191223},{"id":"https://openalex.org/C96314035","wikidata":"https://www.wikidata.org/wiki/Q5282062","display_name":"Discrete system","level":2,"score":0.3369026482105255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24422144889831543},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1823389232158661},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07549440860748291},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0960129507005981","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129507005981","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00151946v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00151946","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science, 2007, 17, pp.261-276. ⟨10.1017/S0960129507005981⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W33980575","https://openalex.org/W71012416","https://openalex.org/W154646596","https://openalex.org/W578108674","https://openalex.org/W1511413932","https://openalex.org/W1596416914","https://openalex.org/W1603574803","https://openalex.org/W1807813576","https://openalex.org/W1975905130","https://openalex.org/W1977738976","https://openalex.org/W1982461707","https://openalex.org/W2039653455","https://openalex.org/W2065513785","https://openalex.org/W2071631329","https://openalex.org/W2102892532","https://openalex.org/W2134120396","https://openalex.org/W2135479785","https://openalex.org/W2148437017","https://openalex.org/W2168711358","https://openalex.org/W2329551434","https://openalex.org/W2486707301","https://openalex.org/W2947056241","https://openalex.org/W3138265894","https://openalex.org/W4237997615","https://openalex.org/W4252713891","https://openalex.org/W4299993032","https://openalex.org/W6661513265","https://openalex.org/W6722500741"],"related_works":["https://openalex.org/W1968317357","https://openalex.org/W2117395819","https://openalex.org/W1993122413","https://openalex.org/W2153388415","https://openalex.org/W2016649807","https://openalex.org/W2890598539","https://openalex.org/W2320278775","https://openalex.org/W2122400977","https://openalex.org/W2037383363","https://openalex.org/W2037438774"],"abstract_inverted_index":{"The":[0],"relationship":[1],"between":[2,77,92],"continuous-time":[3,78],"dynamics":[4],"and":[5,10,18,47,63,80,98],"the":[6,41,48,56,59,74,88],"corresponding":[7],"discrete":[8,99],"schemes,":[9],"its":[11],"generally":[12],"limited":[13],"validity,":[14],"is":[15],"an":[16],"important":[17],"widely":[19],"acknowledged":[20],"field":[21],"within":[22],"numerical":[23,100],"analysis.":[24],"In":[25],"this":[26,35],"paper,":[27],"we":[28],"propose":[29],"another,":[30],"more":[31,89],"physical,":[32],"viewpoint":[33],"on":[34,87],"topic":[36],"in":[37],"order":[38],"to":[39,50],"understand":[40],"possible":[42],"failure":[43],"of":[44,95],"discretisation":[45],"procedures":[46],"way":[49],"fix":[51],"it.":[52],"Three":[53],"basic":[54],"examples,":[55],"logistic":[57],"equation,":[58],"Lotka\u2013Volterra":[60],"predator\u2013prey":[61],"model":[62],"Newton's":[64],"law":[65],"for":[66],"planetary":[67],"motion,":[68],"are":[69],"worked":[70],"out.":[71],"They":[72],"illustrate":[73],"deep":[75],"difference":[76],"evolutions":[79],"discrete-time":[81],"mappings,":[82],"hence":[83],"shedding":[84],"some":[85],"light":[86],"general":[90],"duality":[91],"continuous":[93],"descriptions":[94],"natural":[96],"phenomena":[97],"computations.":[101]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}