{"id":"https://openalex.org/W2807933740","doi":"https://doi.org/10.1142/s0218127418300392","title":"Computing Complex Horseshoes by Means of Piecewise Maps","display_name":"Computing Complex Horseshoes by Means of Piecewise Maps","publication_year":2018,"publication_date":"2018-11-01","ids":{"openalex":"https://openalex.org/W2807933740","doi":"https://doi.org/10.1142/s0218127418300392","mag":"2807933740"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127418300392","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418300392","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.06748","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"\u00c1lvaro G. L\u00f3pez","orcid":null},"institutions":[{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"\u00c1lvaro G. L\u00f3pez","raw_affiliation_strings":["Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]},{"author_position":"middle","author":{"id":null,"display_name":"\u00c1lvar Daza","orcid":null},"institutions":[{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"\u00c1lvar Daza","raw_affiliation_strings":["Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jes\u00fas M. Seoane","orcid":null},"institutions":[{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jes\u00fas M. Seoane","raw_affiliation_strings":["Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]},{"author_position":"last","author":{"id":null,"display_name":"Miguel A. F. Sanju\u00e1n","orcid":null},"institutions":[{"id":"https://openalex.org/I172574986","display_name":"Kaunas University of Technology","ror":"https://ror.org/01me6gb93","country_code":"LT","type":"education","lineage":["https://openalex.org/I172574986"]},{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["ES","LT"],"is_corresponding":false,"raw_author_name":"Miguel A. F. Sanju\u00e1n","raw_affiliation_strings":["Department of Applied Informatics, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania","Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Informatics, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania","institution_ids":["https://openalex.org/I172574986"]},{"raw_affiliation_string":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I182083151"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.06128627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"12","first_page":"1830039","last_page":"1830039"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.6671000123023987,"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"}},"topics":[{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.6671000123023987,"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/T11870","display_name":"Structural Analysis and Optimization","score":0.048900000751018524,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.027899999171495438,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/piecewise","display_name":"Piecewise","score":0.8118000030517578},{"id":"https://openalex.org/keywords/piecewise-linear-manifold","display_name":"Piecewise linear manifold","score":0.5828999876976013},{"id":"https://openalex.org/keywords/horseshoe","display_name":"Horseshoe (symbol)","score":0.5759999752044678},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5235999822616577},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4880000054836273},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.46160000562667847}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8118000030517578},{"id":"https://openalex.org/C184175843","wikidata":"https://www.wikidata.org/wiki/Q7191425","display_name":"Piecewise linear manifold","level":3,"score":0.5828999876976013},{"id":"https://openalex.org/C2778268898","wikidata":"https://www.wikidata.org/wiki/Q5905943","display_name":"Horseshoe (symbol)","level":2,"score":0.5759999752044678},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5527999997138977},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5235999822616577},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4880000054836273},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C2776545253","wikidata":"https://www.wikidata.org/wiki/Q5464292","display_name":"Folding (DSP implementation)","level":2,"score":0.4544000029563904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4284000098705292},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.4212999939918518},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3628999888896942},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2969000041484833},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.27570000290870667},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127418300392","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418300392","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:arXiv.org:1806.06748","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.06748","pdf_url":"https://arxiv.org/pdf/1806.06748","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.06748","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.06748","pdf_url":"https://arxiv.org/pdf/1806.06748","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W2017647225","https://openalex.org/W2022753223","https://openalex.org/W2032259428","https://openalex.org/W2033365799","https://openalex.org/W2055463474","https://openalex.org/W2060143993","https://openalex.org/W2063055007","https://openalex.org/W2072549489","https://openalex.org/W2072769329","https://openalex.org/W2076563167","https://openalex.org/W2085209994","https://openalex.org/W2086126610","https://openalex.org/W2096322542","https://openalex.org/W2102892532","https://openalex.org/W2114703605","https://openalex.org/W2165754425","https://openalex.org/W2315938601","https://openalex.org/W2318999407","https://openalex.org/W2407122018","https://openalex.org/W2412801704","https://openalex.org/W2518649232","https://openalex.org/W2575434776","https://openalex.org/W2963750990","https://openalex.org/W2996433891","https://openalex.org/W4212928962","https://openalex.org/W4229497514"],"related_works":[],"abstract_inverted_index":{"A":[0],"systematic":[1],"procedure":[2],"to":[3,55],"numerically":[4],"compute":[5],"a":[6],"horseshoe":[7,52],"map":[8],"is":[9],"presented.":[10],"This":[11],"new":[12],"method":[13],"uses":[14],"piecewise":[15,53],"functions":[16],"and":[17,32],"expresses":[18],"the":[19,48,67],"required":[20],"operations":[21],"by":[22],"means":[23],"of":[24,50,60],"elementary":[25],"transformations,":[26,38],"such":[27,37],"as":[28,64],"translations,":[29],"scalings,":[30],"projections":[31],"rotations.":[33],"By":[34],"repeatedly":[35],"combining":[36],"arbitrarily":[39],"complex":[40],"folding":[41],"structures":[42],"can":[43],"be":[44],"created.":[45],"We":[46],"show":[47],"potential":[49],"these":[51],"maps":[54],"illustrate":[56],"several":[57],"central":[58],"concepts":[59],"nonlinear":[61],"dynamical":[62],"systems,":[63],"for":[65],"example,":[66],"Wada":[68],"property.":[69]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2018-06-21T00:00:00"}