{"id":"https://openalex.org/W2080829605","doi":"https://doi.org/10.1137/080716736","title":"Semigroups of Affine Groups, Controllability of Affine Systems and Affine Bilinear Systems in $\\mathrm{Sl}(2,\\mathbb{R})\\rtimes\\mathbb{R}^{2}$","display_name":"Semigroups of Affine Groups, Controllability of Affine Systems and Affine Bilinear Systems in $\\mathrm{Sl}(2,\\mathbb{R})\\rtimes\\mathbb{R}^{2}$","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2080829605","doi":"https://doi.org/10.1137/080716736","mag":"2080829605"},"language":"en","primary_location":{"id":"doi:10.1137/080716736","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080716736","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5006900639","display_name":"Osvaldo Germano do Roc\u00edo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Osvaldo G. do Rocio","raw_affiliation_strings":["[email\u00a0protected] and [email\u00a0protected] and [email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected] and [email\u00a0protected] and [email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021681147","display_name":"Alexandre J. Santana","orcid":"https://orcid.org/0000-0003-4944-4844"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexandre J. Santana","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085400206","display_name":"Marcos A. Verdi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcos A. Verdi","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":0.3734,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.55940707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"48","issue":"2","first_page":"1080","last_page":"1088"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9954000115394592,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9954000115394592,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9914000034332275,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9861999750137329,"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/mathematics","display_name":"Mathematics","score":0.8688055276870728},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7037946581840515},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.6758057475090027},{"id":"https://openalex.org/keywords/semidirect-product","display_name":"Semidirect product","score":0.6515276432037354},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4871256351470947},{"id":"https://openalex.org/keywords/affine-representation","display_name":"Affine representation","score":0.48329952359199524},{"id":"https://openalex.org/keywords/complex-space","display_name":"Complex space","score":0.47750991582870483},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4400904178619385},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36615562438964844},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.24136975407600403},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06207653880119324}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8688055276870728},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7037946581840515},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.6758057475090027},{"id":"https://openalex.org/C75066664","wikidata":"https://www.wikidata.org/wiki/Q291126","display_name":"Semidirect product","level":3,"score":0.6515276432037354},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4871256351470947},{"id":"https://openalex.org/C6128414","wikidata":"https://www.wikidata.org/wiki/Q3892887","display_name":"Affine representation","level":5,"score":0.48329952359199524},{"id":"https://openalex.org/C24129628","wikidata":"https://www.wikidata.org/wiki/Q25345430","display_name":"Complex space","level":3,"score":0.47750991582870483},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4400904178619385},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36615562438964844},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.24136975407600403},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06207653880119324},{"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/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.0},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.0},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/080716736","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080716736","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1971064885","https://openalex.org/W2068059759","https://openalex.org/W2083967932","https://openalex.org/W2090377275","https://openalex.org/W2170273734","https://openalex.org/W2180316650","https://openalex.org/W2183143799","https://openalex.org/W2962901843"],"related_works":["https://openalex.org/W1568307077","https://openalex.org/W2036669356","https://openalex.org/W2952605879","https://openalex.org/W1965928613","https://openalex.org/W2354159744","https://openalex.org/W2951782741","https://openalex.org/W2318389742","https://openalex.org/W2962983948","https://openalex.org/W2306105624","https://openalex.org/W2952747335"],"abstract_inverted_index":{"Let":[0],"$G=B\\rtimes":[1],"V$":[2],"be":[3],"an":[4,38],"affine":[5],"group":[6,15],"given":[7],"by":[8],"a":[9,24,42],"semidirect":[10],"product":[11],"of":[12,32,44,46,52],"connected":[13],"Lie":[14],"B":[16,22],"and":[17],"vector":[18],"space":[19],"V,":[20],"where":[21],"has":[23],"transitive":[25],"representation":[26],"on":[27],"V.":[28],"We":[29],"study":[30],"semigroups":[31],"G":[33],"with":[34],"nonempty":[35],"interior.":[36],"As":[37],"application,":[39],"we":[40],"obtain":[41],"characterization":[43],"controllability":[45],"bilinear":[47],"systems":[48],"in":[49],"the":[50],"case":[51],"$\\mathrm{Sl}(2,\\mathbb{R})\\rtimes\\mathbb{R}^{2}$.":[53]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}
