{"id":"https://openalex.org/W4324056439","doi":"https://doi.org/10.1007/s11075-023-01499-9","title":"Sliding modes of high codimension in piecewise-smooth dynamical systems","display_name":"Sliding modes of high codimension in piecewise-smooth dynamical systems","publication_year":2023,"publication_date":"2023-03-13","ids":{"openalex":"https://openalex.org/W4324056439","doi":"https://doi.org/10.1007/s11075-023-01499-9"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-023-01499-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11075-023-01499-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01499-9.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01499-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030219464","display_name":"Nicola Guglielmi","orcid":"https://orcid.org/0000-0003-3795-5225"},"institutions":[{"id":"https://openalex.org/I4210150763","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444","country_code":"IT","type":"education","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210150763"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Nicola Guglielmi","raw_affiliation_strings":["Gran Sasso Science Institute, Viale Francesco Crispi 7, I-67100, L\u2019Aquila, Italy","Gran Sasso Science Institute, Viale Francesco Crispi 7, I-67100, L'Aquila, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gran Sasso Science Institute, Viale Francesco Crispi 7, I-67100, L\u2019Aquila, Italy","institution_ids":["https://openalex.org/I4210150763"]},{"raw_affiliation_string":"Gran Sasso Science Institute, Viale Francesco Crispi 7, I-67100, L'Aquila, Italy","institution_ids":["https://openalex.org/I4210150763"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026173495","display_name":"Ernst Hairer","orcid":"https://orcid.org/0000-0001-5057-2654"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Ernst Hairer","raw_affiliation_strings":["Department de Math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, CH-1211, Geneva 24, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department de Math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, CH-1211, Geneva 24, Switzerland","institution_ids":["https://openalex.org/I114457229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026173495"],"corresponding_institution_ids":["https://openalex.org/I114457229"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":2.8987,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.90387007,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"94","issue":"1","first_page":"257","last_page":"273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9984999895095825,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9818999767303467,"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/T10244","display_name":"Chaos control and synchronization","score":0.9452999830245972,"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/codimension","display_name":"Codimension","score":0.8892594575881958},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.8217964172363281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7496693134307861},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7351374626159668},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.7027354836463928},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6423805356025696},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5865297913551331},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49826502799987793},{"id":"https://openalex.org/keywords/wedge","display_name":"Wedge (geometry)","score":0.4784262776374817},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.46705639362335205},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.46191027760505676},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4247239828109741},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4205961227416992},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.4132623076438904},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3819253146648407},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3361680209636688},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23265117406845093},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09196943044662476}],"concepts":[{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.8892594575881958},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.8217964172363281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7496693134307861},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7351374626159668},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7027354836463928},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6423805356025696},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5865297913551331},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49826502799987793},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.4784262776374817},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.46705639362335205},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.46191027760505676},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4247239828109741},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4205961227416992},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.4132623076438904},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3819253146648407},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3361680209636688},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23265117406845093},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09196943044662476},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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":2,"locations":[{"id":"doi:10.1007/s11075-023-01499-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11075-023-01499-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01499-9.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:unige.ch:aou:unige:180109","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:180109","pdf_url":"https://access.archive-ouverte.unige.ch/access/metadata/988f0b37-b2bc-40ea-9795-1429d8d63895/download","source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1017-1398","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11075-023-01499-9","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11075-023-01499-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01499-9.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323830","display_name":"Universit\u00e9 de Gen\u00e8ve","ror":"https://ror.org/01swzsf04"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4324056439.pdf"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W158518729","https://openalex.org/W1201619888","https://openalex.org/W1964901569","https://openalex.org/W1965225890","https://openalex.org/W1977677836","https://openalex.org/W2003845577","https://openalex.org/W2023233398","https://openalex.org/W2025473712","https://openalex.org/W2028118090","https://openalex.org/W2029273851","https://openalex.org/W2047009410","https://openalex.org/W2076067331","https://openalex.org/W2097121709","https://openalex.org/W2111862827","https://openalex.org/W2569147996","https://openalex.org/W2593063709","https://openalex.org/W3182721126","https://openalex.org/W4212914765","https://openalex.org/W4230708622"],"related_works":["https://openalex.org/W1861797342","https://openalex.org/W2950310075","https://openalex.org/W4366459492","https://openalex.org/W2952962099","https://openalex.org/W2564990357","https://openalex.org/W2771785338","https://openalex.org/W391927469","https://openalex.org/W2011180239","https://openalex.org/W2054350956","https://openalex.org/W2006002535"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"consider":[2],"piecewise-smooth":[3,70],"dynamical":[4,71],"systems,":[5],"i.e.,":[6],"systems":[7,72],"of":[8,16,49,53,69,87,93,96,115],"ordinary":[9],"differential":[10],"equations":[11,17],"switching":[12],"between":[13],"different":[14],"sets":[15],"on":[18,106],"distinct":[19],"domains,":[20],"separated":[21],"by":[22],"hyper-surfaces.":[23,99],"As":[24],"is":[25,79],"well-known,":[26],"when":[27],"the":[28,46,67,83,94,107],"solution":[29,36,55,68,108],"approaches":[30],"a":[31,34,51,88],"discontinuity":[32,77,90,98,113],"manifold,":[33],"classical":[35],"may":[37],"cease":[38],"to":[39,76,112],"exist.":[40],"For":[41],"this":[42],"reason,":[43],"starting":[44],"with":[45],"pioneering":[47],"work":[48,102],"Filippov,":[50],"concept":[52],"weak":[54],"(also":[56],"known":[57],"as":[58],"sliding":[59],"mode)":[60],"has":[61],"been":[62],"introduced":[63],"and":[64,74,110,118],"studied.":[65],"Nowadays,":[66],"in":[73,109],"close":[75,111],"manifolds":[78,114],"well":[80],"understood,":[81],"if":[82],"manifold":[84],"consists":[85],"locally":[86],"single":[89],"hyper-surface":[91],"or":[92],"intersection":[95],"two":[97],"The":[100],"present":[101],"presents":[103],"partial":[104],"results":[105],"codimension":[116],"3":[117],"higher.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}