{"id":"https://openalex.org/W2133057389","doi":"https://doi.org/10.1137/s0363012999361950","title":"On the Global Controllability of Nonlinear Systems: Fountains, Recurrence, and Applications to Hamiltonian Systems","display_name":"On the Global Controllability of Nonlinear Systems: Fountains, Recurrence, and Applications to Hamiltonian Systems","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2133057389","doi":"https://doi.org/10.1137/s0363012999361950","mag":"2133057389"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012999361950","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012999361950","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/A5044187847","display_name":"Peter E. Caines","orcid":"https://orcid.org/0000-0002-5248-9456"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter E. Caines","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5018297962","display_name":"Ekaterina S. Lemch","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ekaterina S. Lemch","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":0.6366,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73577806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"41","issue":"5","first_page":"1532","last_page":"1553"},"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":0.9983999729156494,"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":0.9983999729156494,"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":0.9973000288009644,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.8610971570014954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7964079976081848},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6086385846138},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5887637138366699},{"id":"https://openalex.org/keywords/rank-condition","display_name":"Rank condition","score":0.579325795173645},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.530704915523529},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4691570997238159},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4447990953922272},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.41448405385017395},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35000473260879517},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3293761610984802},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26756197214126587},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22185030579566956},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.19661718606948853},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12066650390625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09762033820152283}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8610971570014954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7964079976081848},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6086385846138},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5887637138366699},{"id":"https://openalex.org/C2778095854","wikidata":"https://www.wikidata.org/wiki/Q4420961","display_name":"Rank condition","level":3,"score":0.579325795173645},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.530704915523529},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4691570997238159},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4447990953922272},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.41448405385017395},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35000473260879517},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3293761610984802},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26756197214126587},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22185030579566956},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.19661718606948853},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12066650390625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09762033820152283},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012999361950","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012999361950","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1484739396","https://openalex.org/W1499788862","https://openalex.org/W1502782630","https://openalex.org/W1540059687","https://openalex.org/W1887006513","https://openalex.org/W1964373008","https://openalex.org/W1975243497","https://openalex.org/W1976364717","https://openalex.org/W1986110911","https://openalex.org/W1987389751","https://openalex.org/W2014305171","https://openalex.org/W2025120273","https://openalex.org/W2034280776","https://openalex.org/W2073454670","https://openalex.org/W2074843442","https://openalex.org/W2113010422","https://openalex.org/W2132783271","https://openalex.org/W2140998418","https://openalex.org/W2143588377","https://openalex.org/W2153026088","https://openalex.org/W2164259133","https://openalex.org/W2988545412","https://openalex.org/W4239216443"],"related_works":["https://openalex.org/W2025554796","https://openalex.org/W2055203360","https://openalex.org/W1975041680","https://openalex.org/W4287775910","https://openalex.org/W2619553900","https://openalex.org/W4294674537","https://openalex.org/W2963040668","https://openalex.org/W4316034888","https://openalex.org/W3032154959","https://openalex.org/W2119276122"],"abstract_inverted_index":{"In":[0],"this":[1,107,136],"paper,":[2],"a":[3,29,83,125,140],"form":[4],"of":[5,28,37,63,66,70,82],"open":[6],"local":[7,87],"accessibility":[8,88],"for":[9,97,124],"nonlinear":[10],"control":[11,72,98,117],"systems":[12,73,100],"is":[13,43,50,54,137],"introduced":[14],"called":[15,74],"the":[16,22,26,46,61,67,80,91,104,131],"continuous":[17,32],"fountain":[18,84],"condition.":[19],"Subject":[20],"to":[21,111,114,129],"conditions":[23,40,123],"that":[24,45,56,120],"(i)":[25,86],"states":[27],"system":[30,47,143],"are":[31,101,109],"fountains":[33],"and":[34,85,89],"(ii)":[35,90],"one":[36],"various":[38],"recurrence":[39],"holds,":[41],"it":[42],"established":[44],"state":[48,68],"space":[49,69],"(globally)":[51],"controllable.":[52],"It":[53],"shown":[55,110],"these":[57],"controllability":[58,62,134],"results":[59,105],"imply":[60],"certain":[64],"subsets":[65],"Hamiltonian":[71],"energy":[75],"slices.":[76],"The":[77],"relations":[78],"between":[79],"notion":[81],"full":[92],"Lie":[93],"algebra":[94],"rank":[95],"condition":[96],"affine":[99],"investigated.":[102],"Finally,":[103],"in":[106,119],"paper":[108],"have":[112],"application":[113],"hierarchical":[115],"hybrid":[116],"theory":[118],"they":[121],"give":[122],"finite":[126],"analytic":[127],"partition":[128],"satisfy":[130],"so-called":[132],"in-block":[133],"property;":[135],"illustrated":[138],"with":[139],"linear":[141],"mass-spring":[142],"example.":[144]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
