{"id":"https://openalex.org/W2568539733","doi":"https://doi.org/10.48550/arxiv.1701.00670","title":"Intrinsic and Apparent Singularities in Flat Differential Systems","display_name":"Intrinsic and Apparent Singularities in Flat Differential Systems","publication_year":2017,"publication_date":"2017-01-03","ids":{"openalex":"https://openalex.org/W2568539733","doi":"https://doi.org/10.48550/arxiv.1701.00670","mag":"2568539733"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1701.00670","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.00670","pdf_url":"https://arxiv.org/pdf/1701.00670","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"},"parent_works":[],"lineage":["https://openalex.org/W2568539733"],"child_works_count":0,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1701.00670","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009998596","display_name":"Yirmeyahu J. Kaminski","orcid":"https://orcid.org/0000-0001-5438-6963","observed_orcids":["https://orcid.org/0000-0001-5438-6963"]},"institutions":[{"id":"https://openalex.org/I157943965","display_name":"Holon Institute of Technology","ror":"https://ror.org/02prqh017","country_code":"IL","type":"education","lineage":["https://openalex.org/I157943965"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Kaminski, Y. J.","raw_affiliation_strings":["Department of Applied Mathematics , Holon Institute of Technology , Holon , Israel,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , Holon Institute of Technology , Holon , Israel,","institution_ids":["https://openalex.org/I157943965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084436469","display_name":"Jean L\u00e9vine","orcid":"https://orcid.org/0000-0002-8095-4132","observed_orcids":["https://orcid.org/0000-0002-8095-4132"]},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I4405253953","display_name":"Centre Automatique et Syst\u00e8mes","ror":"https://ror.org/018786988","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4405253953","https://openalex.org/I70768539"]},{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Levine, J.","raw_affiliation_strings":["CAS , Unit\u00e9 Maths et Syst\u00e8mes , MINES-ParisTech , PSL Research University , 60 Bd Saint-Michel , 75272 Paris Cedex 06 , France,","Centre Automatique et Syst\u00e8mes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CAS , Unit\u00e9 Maths et Syst\u00e8mes , MINES-ParisTech , PSL Research University , 60 Bd Saint-Michel , 75272 Paris Cedex 06 , France,","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I4405253953","https://openalex.org/I70768539"]},{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes","institution_ids":["https://openalex.org/I4405253953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065656637","display_name":"Fran\u00e7ois Ollivier","orcid":"https://orcid.org/0000-0002-4309-3791","observed_orcids":["https://orcid.org/0000-0002-4309-3791"]},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ollivier, F.","raw_affiliation_strings":["LIX , \u00c9cole Polytechnique , 91128 Palaiseau Cedex , France,","Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIX , \u00c9cole Polytechnique , 91128 Palaiseau Cedex , France,","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210139461"]},{"raw_affiliation_string":"Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau]","institution_ids":["https://openalex.org/I4210139461"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.8446999788284302,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.8446999788284302,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.10890000313520432,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.015200000256299973,"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/flat-systems","display_name":"flat systems","score":0.8140000104904175},{"id":"https://openalex.org/keywords/flat-outputs","display_name":"flat outputs","score":0.847000002861023},{"id":"https://openalex.org/keywords/apparent-singularities","display_name":"apparent singularities","score":1.0},{"id":"https://openalex.org/keywords/global-motion-planning","display_name":"global motion planning","score":0.7080000042915344},{"id":"https://openalex.org/keywords/trajectory-planning","display_name":"trajectory planning","score":0.7170000076293945}],"concepts":[{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.8487022519111633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6521643996238708},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.570806622505188},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5376831889152527},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5234193801879883},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.49134722352027893},{"id":"https://openalex.org/C2777964439","wikidata":"https://www.wikidata.org/wiki/Q5884201","display_name":"Holonomic","level":2,"score":0.49060288071632385},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46856358647346497},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.4629970192909241},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44066834449768066},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.4333249628543854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37953805923461914},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30434224009513855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16356700658798218},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15120142698287964},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.12359443306922913},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06836822628974915},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1701.00670","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.00670","pdf_url":"https://arxiv.org/pdf/1701.00670","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:HAL:hal-01426378v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-01426378","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2017","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.1701.00670","doi":"https://doi.org/10.48550/arxiv.1701.00670","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1701.00670","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":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1701.00670","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.00670","pdf_url":"https://arxiv.org/pdf/1701.00670","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2568539733.pdf","grobid_xml":"https://content.openalex.org/works/W2568539733.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W46795629","https://openalex.org/W2059473649","https://openalex.org/W2065297540","https://openalex.org/W2073761272","https://openalex.org/W2112396687","https://openalex.org/W2165063889","https://openalex.org/W2596296327","https://openalex.org/W4232303308"],"related_works":["https://openalex.org/W2793319668","https://openalex.org/W3013218223","https://openalex.org/W4298206550","https://openalex.org/W1588279583","https://openalex.org/W1809619944","https://openalex.org/W1988964956","https://openalex.org/W2767655842","https://openalex.org/W769986308","https://openalex.org/W134054258","https://openalex.org/W4383066389"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,177],"study":[4],"the":[5,13,19,28,43,94,97,104,130,149,152,188],"singularities":[6,128],"of":[7,18,30,42,45,70,74,96,137,144,151,155,157,187,191],"locally":[8,39],"flat":[9,34,86,115],"systems,":[10,26],"motivated":[11],"by":[12,81],"solution,":[14],"if":[15],"it":[16,109],"exists,":[17],"global":[20,184],"motion":[21,185],"planning":[22,62,186],"problem":[23],"for":[24],"such":[25],"in":[27,106,142,148],"spirit":[29],"\\cite{CE_14}.":[31],"More":[32],"precisely,":[33],"outputs":[35,116],"may":[36],"be":[37,55,77],"only":[38],"defined":[40,88,102],"because":[41],"existence":[44],"points":[46,68,126,139],"where":[47],"they":[48],"are":[49,69],"singular":[50,85],"(a":[51],"notion":[52],"that":[53,112],"will":[54],"made":[56],"clear":[57],"later),":[58],"thus":[59],"preventing":[60],"from":[61],"trajectories":[63],"crossing":[64],"these":[65,125,138],"points.":[66,122],"Such":[67],"different":[71],"types.":[72],"Some":[73],"them":[75],"can":[76],"easily":[78],"ruled":[79],"out":[80],"considering":[82],"another":[83],"non":[84,192],"output,":[87],"on":[89],"an":[90],"open":[91],"set":[92],"intersecting":[93],"domain":[95],"former":[98],"one":[99],"and":[100,129,146,160],"well":[101],"at":[103,118,120],"point":[105],"question.":[107],"However,":[108],"might":[110],"happen":[111],"no":[113],"well-defined":[114],"exist":[117],"all":[119],"some":[121],"We":[123,165],"call":[124],"\\emph{intrinsic}":[127],"other":[131],"ones":[132],"\\emph{apparent}.":[133],"A":[134],"rigorous":[135],"defintion":[136],"is":[140],"introduced":[141],"terms":[143],"atlas":[145],"charts":[147],"framework":[150],"differential":[153],"geometry":[154],"jets":[156],"infinite":[158],"order":[159],"Lie-B\u00e4cklund":[161],"isomorphisms":[162],"(see":[163],"\\cite{FLMR_99,Levine-09}).":[164],"then":[166],"give":[167],"a":[168],"criterion":[169],"allowing":[170],"to":[171,183],"effectively":[172],"compute":[173],"intrinsic":[174],"singularities.":[175],"Finally,":[176],"show":[178],"how":[179],"our":[180],"results":[181],"apply":[182],"well-known":[189],"example":[190],"holonomic":[193],"car.":[194]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2017-01-13T00:00:00"}
