{"id":"https://openalex.org/W1984013014","doi":"https://doi.org/10.1137/080743123","title":"The Dynamics of Regularized Discontinuous Maps with Applications to Impacting Systems","display_name":"The Dynamics of Regularized Discontinuous Maps with Applications to Impacting Systems","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1984013014","doi":"https://doi.org/10.1137/080743123","mag":"1984013014"},"language":"en","primary_location":{"id":"doi:10.1137/080743123","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080743123","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":["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/A5035287810","display_name":"Stephen Pring","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. R. Pring","raw_affiliation_strings":["S.R.Pring@bath.ac.uk and C.J.Budd@bath.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"S.R.Pring@bath.ac.uk and C.J.Budd@bath.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021625363","display_name":"Chris Budd","orcid":"https://orcid.org/0000-0003-4536-1662"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. J. Budd","raw_affiliation_strings":["Department of Mathematical Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8883,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90873833,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"1","first_page":"188","last_page":"219"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9926999807357788,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9926999807357788,"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9821000099182129,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10244","display_name":"Chaos control and synchronization","score":0.9767000079154968,"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/bifurcation","display_name":"Bifurcation","score":0.5965522527694702},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.5851476788520813},{"id":"https://openalex.org/keywords/period","display_name":"Period (music)","score":0.5636439323425293},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5239172577857971},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5231688618659973},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5111666321754456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47347915172576904},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.4198686182498932},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40270429849624634},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38769960403442383},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33767881989479065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32885223627090454},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2735127806663513},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1795104742050171},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06505778431892395}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5965522527694702},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5851476788520813},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.5636439323425293},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5239172577857971},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5231688618659973},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5111666321754456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47347915172576904},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.4198686182498932},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40270429849624634},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38769960403442383},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33767881989479065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32885223627090454},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2735127806663513},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1795104742050171},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06505778431892395},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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:10.1137/080743123","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080743123","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1552277675","https://openalex.org/W1596227557","https://openalex.org/W1970311793","https://openalex.org/W1971396077","https://openalex.org/W1972227521","https://openalex.org/W2010181515","https://openalex.org/W2011227277","https://openalex.org/W2013456332","https://openalex.org/W2014534896","https://openalex.org/W2019383201","https://openalex.org/W2020783811","https://openalex.org/W2021929396","https://openalex.org/W2031604902","https://openalex.org/W2039117252","https://openalex.org/W2040317361","https://openalex.org/W2047494798","https://openalex.org/W2065773966","https://openalex.org/W2080761408","https://openalex.org/W2096886711","https://openalex.org/W2103959724","https://openalex.org/W2148764917","https://openalex.org/W4246664411"],"related_works":["https://openalex.org/W2060450020","https://openalex.org/W2014696479","https://openalex.org/W2095274406","https://openalex.org/W2271295025","https://openalex.org/W4321135758","https://openalex.org/W1898914577","https://openalex.org/W2167230766","https://openalex.org/W139684681","https://openalex.org/W1983047697","https://openalex.org/W2356929285"],"abstract_inverted_index":{"One-dimensional":[0],"piecewise-smooth":[1],"discontinuous":[2,46,55,68,102,109],"maps":[3,56,69,78],"(maps":[4],"with":[5,17],"gaps)":[6],"are":[7,62],"known":[8],"to":[9,42,54,114,147,149],"have":[10],"surprisingly":[11],"rich":[12],"dynamics,":[13],"including":[14],"periodic":[15],"orbits":[16],"very":[18,51],"high":[19],"period":[20,156],"and":[21,57,93,111,131],"bifurcation":[22],"diagrams":[23],"showing":[24],"period-adding":[25,130],"or":[26],"period-incrementing":[27,132],"behavior.":[28],"In":[29],"this":[30,113],"paper":[31],"we":[32,40,80,123,128],"study":[33,81,104],"a":[34,150],"new":[35],"class":[36],"of":[37,74,85,101,107,117,143,153],"maps,":[38,47,103,110],"which":[39,122],"refer":[41],"as":[43,72],"regularized":[44,67,108],"one-dimensional":[45],"because":[48],"they":[49],"give":[50],"similar":[52],"dynamics":[53,84,100,106],"closely":[58],"approximate":[59],"them,":[60],"yet":[61],"continuous.":[63],"We":[64,97,125],"show":[65,126],"that":[66,127,140],"arise":[70],"naturally":[71],"limits":[73],"higher":[75,155],"dimensional":[76],"continuous":[77],"when":[79],"the":[82,90,94,99,105,115,118,141,144,154],"global":[83],"two":[86,119,136],"nonsmooth":[87],"mechanical":[88,120],"applications:":[89],"cam-follower":[91],"system":[92],"impact":[95],"oscillator.":[96],"review":[98],"compare":[112],"behavior":[116,133],"applications":[121],"model.":[124],"observe":[129],"in":[134],"these":[135],"systems":[137],"respectively":[138],"but":[139],"effect":[142],"regularization":[145],"is":[146],"lead":[148],"progressive":[151],"loss":[152],"orbits.":[157]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
