{"id":"https://openalex.org/W4281615737","doi":"https://doi.org/10.1137/20m1387730","title":"Angular Values of Nonautonomous and Random Linear Dynamical Systems: Part I---Fundamentals","display_name":"Angular Values of Nonautonomous and Random Linear Dynamical Systems: Part I---Fundamentals","publication_year":2022,"publication_date":"2022-05-31","ids":{"openalex":"https://openalex.org/W4281615737","doi":"https://doi.org/10.1137/20m1387730"},"language":"en","primary_location":{"id":"doi:10.1137/20m1387730","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1387730","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2012.11305","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110164030","display_name":"Wolf\u2010J\u00fcrgen Beyn","orcid":null},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Wolf-J\u00fcrgen Beyn","raw_affiliation_strings":["Department of Mathematics, Bielefeld University, 33501 Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bielefeld University, 33501 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016233400","display_name":"Gary Froyland","orcid":"https://orcid.org/0000-0002-2995-0582"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Gary Froyland","raw_affiliation_strings":["School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062564873","display_name":"Thorsten H\u00fcls","orcid":null},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thorsten H\u00fcls","raw_affiliation_strings":["Department of Mathematics, Bielefeld University, 33501 Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bielefeld University, 33501 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4881,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59931598,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"21","issue":"2","first_page":"1245","last_page":"1286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9995999932289124,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991999864578247,"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/T10244","display_name":"Chaos control and synchronization","score":0.9973000288009644,"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5112738609313965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5072295665740967},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45395416021347046},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3641700744628906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33665046095848083},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2842079997062683}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5112738609313965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5072295665740967},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45395416021347046},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3641700744628906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33665046095848083},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2842079997062683},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/20m1387730","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1387730","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2012.11305","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.11305","pdf_url":"https://arxiv.org/pdf/2012.11305","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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:pub.uni-bielefeld.de:2964602","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2964602","pdf_url":null,"source":{"id":"https://openalex.org/S4306401624","display_name":"Publikationen an der Universit\u00e4t Bielefeld (Universit\u00e4t Bielefeld)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2012.11305","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.11305","pdf_url":"https://arxiv.org/pdf/2012.11305","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[{"id":"https://openalex.org/G1031765108","display_name":null,"funder_award_id":"CRC 701","funder_id":"https://openalex.org/F4320323389","funder_display_name":"Universit\u00e4t Bielefeld"},{"id":"https://openalex.org/G7121511148","display_name":null,"funder_award_id":"CRC 1283","funder_id":"https://openalex.org/F4320323389","funder_display_name":"Universit\u00e4t Bielefeld"}],"funders":[{"id":"https://openalex.org/F4320320965","display_name":"University of New South Wales","ror":"https://ror.org/03r8z3t63"},{"id":"https://openalex.org/F4320323389","display_name":"Universit\u00e4t Bielefeld","ror":"https://ror.org/02hpadn98"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1963815527","https://openalex.org/W1973683994","https://openalex.org/W1975277883","https://openalex.org/W1985055569","https://openalex.org/W1994294813","https://openalex.org/W1999026968","https://openalex.org/W2001376754","https://openalex.org/W2008191112","https://openalex.org/W2009515427","https://openalex.org/W2009985633","https://openalex.org/W2023605401","https://openalex.org/W2031648707","https://openalex.org/W2032703442","https://openalex.org/W2035492228","https://openalex.org/W2061444724","https://openalex.org/W2094879944","https://openalex.org/W2125566231","https://openalex.org/W2149380762","https://openalex.org/W2556522540","https://openalex.org/W2597903068","https://openalex.org/W3102873796"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"We":[0,17,149],"introduce":[1],"the":[2,19,79,90,138,143,146,151],"notion":[3,106],"of":[4,24,42,57,82,107,125,131,137,145],"angular":[5,49,58,75,108,161,172],"values":[6,59,76,109,173],"for":[7,64,85,160,170],"deterministic":[8],"linear":[9,15,34],"difference":[10],"equations":[11],"and":[12,60,95,128,163],"ran-":[13],"dom":[14],"cocycles.":[16],"measure":[18],"principal":[20,44],"angles":[21],"between":[22,54],"subspaces":[23,70,115,130],"fixed":[25],"dimension":[26,127],"as":[27],"they":[28],"evolve":[29],"under":[30],"nonautonomous":[31],"or":[32],"random":[33,65],"dynamics.":[35],"The":[36,134],"focus":[37],"is":[38],"on":[39],"long-term":[40],"averages":[41],"these":[43],"angles,":[45],"which":[46],"we":[47,51],"call":[48],"values:":[50],"demonstrate":[52],"relationships":[53],"different":[55],"types":[56],"prove":[61],"their":[62],"existence":[63],"dynamical":[66,123],"systems.":[67],"For":[68],"one-dimensional":[69],"in":[71],"two-dimensional":[72],"systems":[73,124],"our":[74,105,119],"agree":[77],"with":[78],"classical":[80],"theory":[81,144],"rotation":[83],"numbers":[84],"orientation-preserving":[86],"circle":[87],"homeomorphisms":[88],"if":[89],"matrix":[91],"has":[92],"positive":[93],"determinant":[94],"does":[96],"not":[97],"rotate":[98],"vectors":[99],"by":[100,112],"more":[101],"than":[102,117],"$\\frac{\\pi}{2}$.":[103],"Because":[104],"ignores":[110],"orientation":[111],"looking":[113],"at":[114],"rather":[116],"vectors,":[118],"results":[120],"apply":[121],"to":[122,129,153],"any":[126],"arbitrary":[132],"dimension.":[133],"second":[135],"part":[136],"paper":[139],"delves":[140],"deeper":[141],"into":[142],"autonomous":[147],"case.":[148],"explore":[150],"relation":[152],"(generalized)":[154],"eigenspaces,":[155],"provide":[156],"some":[157],"explicit":[158],"formulas":[159],"values,":[162],"set":[164],"up":[165],"a":[166],"general":[167],"numerical":[168],"algorithm":[169],"computing":[171],"via":[174],"Schur":[175],"decompositions.":[176]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}