{"id":"https://openalex.org/W4414309110","doi":"https://doi.org/10.1142/s0218127425300307","title":"Abundance of Weird Quasiperiodic Attractors in Piecewise Linear Discontinuous Maps","display_name":"Abundance of Weird Quasiperiodic Attractors in Piecewise Linear Discontinuous Maps","publication_year":2025,"publication_date":"2025-09-17","ids":{"openalex":"https://openalex.org/W4414309110","doi":"https://doi.org/10.1142/s0218127425300307"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425300307","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425300307","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5045586765","display_name":"Laura Gardini","orcid":"https://orcid.org/0000-0002-3386-6543"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]},{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"education","lineage":["https://openalex.org/I190397597"]}],"countries":["CZ","IT"],"is_corresponding":false,"raw_author_name":"Laura Gardini","raw_affiliation_strings":["Department of Economics, Society and Politics, University of Urbino Carlo Bo, 61029 Urbino, Italy","Department of Finance, V\u0160B \u2013 Technical University of Ostrava, 708 00 Ostrava, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-3386-6543","affiliations":[{"raw_affiliation_string":"Department of Economics, Society and Politics, University of Urbino Carlo Bo, 61029 Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]},{"raw_affiliation_string":"Department of Finance, V\u0160B \u2013 Technical University of Ostrava, 708 00 Ostrava, Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034975789","display_name":"Davide Radi","orcid":"https://orcid.org/0000-0001-7809-1166"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]},{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["CZ","IT"],"is_corresponding":false,"raw_author_name":"Davide Radi","raw_affiliation_strings":["Department of Finance, V\u0160B \u2013 Technical University of Ostrava, 708 00 Ostrava, Czech Republic","Department of Mathematics for Economic, Financial and Actuarial Sciences, Catholic University of Milan, 20123 Milan, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7809-1166","affiliations":[{"raw_affiliation_string":"Department of Finance, V\u0160B \u2013 Technical University of Ostrava, 708 00 Ostrava, Czech Republic","institution_ids":["https://openalex.org/I142208455"]},{"raw_affiliation_string":"Department of Mathematics for Economic, Financial and Actuarial Sciences, Catholic University of Milan, 20123 Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085576419","display_name":"Iryna Sushko","orcid":"https://orcid.org/0000-0001-5879-0699"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]},{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["IT","UA"],"is_corresponding":false,"raw_author_name":"Iryna Sushko","raw_affiliation_strings":["Department of Mathematics for Economic, Financial and Actuarial Sciences, Catholic University of Milan, 20123 Milan, Italy","Institute of Mathematics, NAS of Ukraine, 01024 Kyiv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0001-5879-0699","affiliations":[{"raw_affiliation_string":"Department of Mathematics for Economic, Financial and Actuarial Sciences, Catholic University of Milan, 20123 Milan, Italy","institution_ids":["https://openalex.org/I189158943"]},{"raw_affiliation_string":"Institute of Mathematics, NAS of Ukraine, 01024 Kyiv, Ukraine","institution_ids":["https://openalex.org/I190444043"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071860051","display_name":"Noemi Schmitt","orcid":null},"institutions":[{"id":"https://openalex.org/I94626330","display_name":"University of Bamberg","ror":"https://ror.org/01c1w6d29","country_code":"DE","type":"education","lineage":["https://openalex.org/I94626330"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Noemi Schmitt","raw_affiliation_strings":["Department of Economics, University of Bamberg, D-96047 Bamberg, Germany"],"raw_orcid":"https://orcid.org/0009-0004-6424-8889","affiliations":[{"raw_affiliation_string":"Department of Economics, University of Bamberg, D-96047 Bamberg, Germany","institution_ids":["https://openalex.org/I94626330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088202203","display_name":"Frank Westerhoff","orcid":"https://orcid.org/0000-0003-1666-4103"},"institutions":[{"id":"https://openalex.org/I94626330","display_name":"University of Bamberg","ror":"https://ror.org/01c1w6d29","country_code":"DE","type":"education","lineage":["https://openalex.org/I94626330"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank Westerhoff","raw_affiliation_strings":["Department of Economics, University of Bamberg, D-96047 Bamberg, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1666-4103","affiliations":[{"raw_affiliation_string":"Department of Economics, University of Bamberg, D-96047 Bamberg, Germany","institution_ids":["https://openalex.org/I94626330"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2728,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.93139694,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"35","issue":"15","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9955000281333923,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9916999936103821,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.8881999850273132},{"id":"https://openalex.org/keywords/quasiperiodic-function","display_name":"Quasiperiodic function","score":0.8802000284194946},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.6733999848365784},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.619700014591217},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5328999757766724},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4677000045776367},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.46149998903274536},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4018999934196472}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8881999850273132},{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.8802000284194946},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6995000243186951},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.6733999848365784},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.619700014591217},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5328999757766724},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.46149998903274536},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.392300009727478},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38920000195503235},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3619000017642975},{"id":"https://openalex.org/C21955772","wikidata":"https://www.wikidata.org/wiki/Q339199","display_name":"Poincar\u00e9 map","level":4,"score":0.3246000111103058},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C21550011","wikidata":"https://www.wikidata.org/wiki/Q7632143","display_name":"Substitution tiling","level":2,"score":0.29089999198913574},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.27630001306533813},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.27619999647140503},{"id":"https://openalex.org/C184175843","wikidata":"https://www.wikidata.org/wiki/Q7191425","display_name":"Piecewise linear manifold","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127425300307","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425300307","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3219465071","display_name":null,"funder_award_id":"22-28882S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G4735692255","display_name":null,"funder_award_id":"CZ.10.03.01/00/22 003/000004","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1970495888","https://openalex.org/W1979301398","https://openalex.org/W1996324887","https://openalex.org/W2002442930","https://openalex.org/W2009246623","https://openalex.org/W2025855743","https://openalex.org/W2048255646","https://openalex.org/W2061194688","https://openalex.org/W2079561663","https://openalex.org/W2083968850","https://openalex.org/W2114901255","https://openalex.org/W2118395206","https://openalex.org/W2129721454","https://openalex.org/W2144355454","https://openalex.org/W2145782975","https://openalex.org/W2146046397","https://openalex.org/W2155329432","https://openalex.org/W2500622636","https://openalex.org/W2546743372","https://openalex.org/W2572944242","https://openalex.org/W2903456461","https://openalex.org/W2951058880","https://openalex.org/W2966092015","https://openalex.org/W2974380649","https://openalex.org/W2990234538","https://openalex.org/W4230378422","https://openalex.org/W4292510609","https://openalex.org/W4293873725","https://openalex.org/W4391872880","https://openalex.org/W4392501022","https://openalex.org/W4393049883","https://openalex.org/W4394619913","https://openalex.org/W4396688030","https://openalex.org/W4399570848","https://openalex.org/W4409891860","https://openalex.org/W4411682253","https://openalex.org/W4412819920","https://openalex.org/W4413407298"],"related_works":[],"abstract_inverted_index":{"In":[0,210],"this":[1,235],"work,":[2],"we":[3,39,213],"consider":[4,97],"a":[5,19,25,119,132,146,189],"class":[6,48,202],"of":[7,22,49,57,63,115,121,163,174,183,196,221,234,238],"n-dimensional,":[8],"[Formula:":[9],"see":[10],"text],":[11],"piecewise":[12,133],"linear":[13,134],"discontinuous":[14],"maps":[15,51,85,199],"that":[16,41,72,105,198],"can":[17,203],"exhibit":[18],"new":[20,236],"type":[21,237],"attractor,":[23,139,149],"called":[24],"weird":[26,147],"quasiperiodic":[27,148],"attractor.":[28],"While":[29],"the":[30,76,79,92,98,109,112,116,126,142,161,194,219,229],"dynamics":[31],"associated":[32],"with":[33,153,171,180],"these":[34,164,222],"attractors":[35,43,155,165],"may":[36,151],"appear":[37],"chaotic,":[38],"prove":[40,104],"chaotic":[42],"cannot":[44,86],"occur.":[45],"The":[46,66,137],"considered":[47],"n-dimensional":[50],"allows":[52],"for":[53,242],"any":[54],"finite":[55],"number":[56],"partitions,":[58],"separated":[59],"by":[60],"various":[61],"types":[62,173,182],"discontinuity":[64,184],"sets.":[65,158,185],"key":[67],"characteristic,":[68],"beyond":[69],"discontinuity,":[70],"is":[71,129,145],"all":[73],"functions":[74,170],"defining":[75],"map":[77,117],"have":[78,87],"same":[80],"real":[81],"fixed":[82,93,127,143],"point.":[83],"These":[84],"hyperbolic":[88],"cycles":[89],"other":[90,154],"than":[91],"point":[94,128],"itself.":[95],"We":[96,103,159,224],"two-dimensional":[99],"case":[100],"in":[101,106,200,228],"detail.":[102],"nongeneric":[107],"cases,":[108,212],"restriction,":[110],"or":[111,156],"first":[113],"return,":[114],"to":[118,131,188,206,218],"segment":[120],"straight":[122],"line":[123],"issuing":[124],"from":[125,141],"reducible":[130],"circle":[135],"map.":[136],"generic":[138],"different":[140,172,181],"point,":[144],"which":[150],"coexist":[152],"attracting":[157],"illustrate":[160],"existence":[162],"through":[166],"numerous":[167],"examples,":[168],"using":[169],"Jacobian":[175],"matrices,":[176],"as":[177,179],"well":[178],"An":[186],"application":[187],"financial":[190],"market":[191],"modeling":[192],"shows":[193],"role":[195],"regulator":[197],"our":[201],"have,":[204],"leading":[205,217],"endogenous":[207],"nonregular":[208],"dynamics.":[209],"some":[211],"describe":[214],"possible":[215],"mechanisms":[216],"appearance":[220],"attractors.":[223],"also":[225],"give":[226],"examples":[227],"three-dimensional":[230],"space.":[231],"Several":[232],"properties":[233],"attractor":[239],"remain":[240],"open":[241],"further":[243],"investigation.":[244]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}