{"id":"https://openalex.org/W2025145600","doi":"https://doi.org/10.1142/s0218127405014192","title":"SLOW\u2013FAST DYNAMICS GENERATED BY NONINVERTIBLE PLANE MAPS","display_name":"SLOW\u2013FAST DYNAMICS GENERATED BY NONINVERTIBLE PLANE MAPS","publication_year":2005,"publication_date":"2005-11-01","ids":{"openalex":"https://openalex.org/W2025145600","doi":"https://doi.org/10.1142/s0218127405014192","mag":"2025145600"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405014192","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014192","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/A5108428626","display_name":"Christian Mira","orcid":null},"institutions":[{"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":["IT"],"is_corresponding":false,"raw_author_name":"CHRISTIAN MIRA","raw_affiliation_strings":["19 rue d'Occitanie, 31130 Quint Fonsegrives, France","Istituto di Scienze Economiche, University of Urbino, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"19 rue d'Occitanie, 31130 Quint Fonsegrives, France","institution_ids":[]},{"raw_affiliation_string":"Istituto di Scienze Economiche, University of Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023386693","display_name":"Andrey Shilnikov","orcid":"https://orcid.org/0000-0002-4879-4327"},"institutions":[{"id":"https://openalex.org/I181565077","display_name":"Georgia State University","ror":"https://ror.org/03qt6ba18","country_code":"US","type":"education","lineage":["https://openalex.org/I181565077"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ANDREY SHILNIKOV","raw_affiliation_strings":["Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA","Department of Mathematics and Statistics , Georgia State University , Atlanta , GA 30303 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA","institution_ids":["https://openalex.org/I181565077"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , Georgia State University , Atlanta , GA 30303 , USA","institution_ids":["https://openalex.org/I181565077"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2268,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.53213456,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"15","issue":"11","first_page":"3509","last_page":"3534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9977999925613403,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9977999925613403,"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/T10244","display_name":"Chaos control and synchronization","score":0.9937000274658203,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7207412123680115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6500662565231323},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6056170463562012},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5778632164001465},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5764041543006897},{"id":"https://openalex.org/keywords/phase-plane","display_name":"Phase plane","score":0.5501346588134766},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5289090871810913},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.47248902916908264},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4507012367248535},{"id":"https://openalex.org/keywords/complex-dynamics","display_name":"Complex dynamics","score":0.4199768900871277},{"id":"https://openalex.org/keywords/julia-set","display_name":"Julia set","score":0.4185701906681061},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.348522812128067},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3108982443809509},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2584274411201477},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19164204597473145},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13892659544944763},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.08769354224205017}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7207412123680115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6500662565231323},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6056170463562012},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5778632164001465},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5764041543006897},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.5501346588134766},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5289090871810913},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.47248902916908264},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4507012367248535},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.4199768900871277},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.4185701906681061},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.348522812128067},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3108982443809509},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2584274411201477},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19164204597473145},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13892659544944763},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08769354224205017},{"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127405014192","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014192","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.706.8496","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.706.8496","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ni.gsu.edu/%7Eashilnikov/research/ShilniMi.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W567049363","https://openalex.org/W620067635","https://openalex.org/W649457022","https://openalex.org/W1565264866","https://openalex.org/W1597461812","https://openalex.org/W1974302683","https://openalex.org/W1986404173","https://openalex.org/W1995784407","https://openalex.org/W2016767879","https://openalex.org/W2035246107","https://openalex.org/W2087934695","https://openalex.org/W2088287925","https://openalex.org/W2109676432","https://openalex.org/W4250146611","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W862474055","https://openalex.org/W2413336514","https://openalex.org/W4321499576","https://openalex.org/W4240246673","https://openalex.org/W3005594646","https://openalex.org/W1412314251","https://openalex.org/W2486937119","https://openalex.org/W2037914258","https://openalex.org/W2435945757","https://openalex.org/W1595367867"],"abstract_inverted_index":{"The":[0,69],"present":[1],"paper":[2],"focuses":[3],"on":[4],"the":[5,36,48,58,79,99],"two":[6],"time":[7],"scale":[8],"dynamics":[9],"generated":[10],"by":[11,108],"2D":[12],"polynomial":[13],"noninvertible":[14,32],"maps":[15,110],"T":[16],"of":[17,60,66,72,81,101],"(Z0":[18],"-":[19,23,25],"Z2)":[20],"and":[21,62,83,104],"(Z1":[22],"Z3":[24],"Z1)":[26],"types.":[27],"This":[28],"symbolism,":[29],"specific":[30],"to":[31],"maps,":[33],"means":[34],"that":[35],"phase":[37],"plane":[38],"is":[39,57],"partitioned":[40],"into":[41,91],"zones":[42],"Zk,":[43],"where":[44],"each":[45],"point":[46],"possesses":[47],"k":[49],"real":[50],"rank-one":[51],"preimages.":[52],"Of":[53],"special":[54],"interest":[55],"here":[56],"structure":[59],"slow":[61,84],"fast":[63,82],"motion":[64],"sets":[65],"such":[67,109],"maps.":[68],"formation":[70],"mechanism":[71],"a":[73,92],"stable":[74],"invariant":[75],"close":[76],"curve":[77],"through":[78],"interaction":[80],"dynamics,":[85],"as":[86,88,113],"well":[87],"its":[89],"transformation":[90],"canard":[93],"are":[94,111],"studied.":[95],"A":[96],"few":[97],"among":[98],"plethora":[100],"chaotic":[102,105],"attractors":[103],"transients":[106],"produced":[107],"described":[112],"well.":[114]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"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":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}