{"id":"https://openalex.org/W2807897117","doi":"https://doi.org/10.3390/sym10060211","title":"Dynamics on Binary Relations over Topological Spaces","display_name":"Dynamics on Binary Relations over Topological Spaces","publication_year":2018,"publication_date":"2018-06-11","ids":{"openalex":"https://openalex.org/W2807897117","doi":"https://doi.org/10.3390/sym10060211","mag":"2807897117"},"language":"en","primary_location":{"id":"doi:10.3390/sym10060211","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10060211","pdf_url":"https://www.mdpi.com/2073-8994/10/6/211/pdf?version=1528706989","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/10/6/211/pdf?version=1528706989","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055201977","display_name":"Chung-Chuan Chen","orcid":"https://orcid.org/0000-0003-4297-3305"},"institutions":[{"id":"https://openalex.org/I34574549","display_name":"National Taichung University of Education","ror":"https://ror.org/006tnfe02","country_code":"TW","type":"education","lineage":["https://openalex.org/I34574549"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chung-Chuan Chen","raw_affiliation_strings":["Department of Mathematics Education, National Taichung University of Education, Taichung 403, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, National Taichung University of Education, Taichung 403, Taiwan","institution_ids":["https://openalex.org/I34574549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079829006","display_name":"J. Alberto Conejero","orcid":"https://orcid.org/0000-0003-3681-7533"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J. Alberto Conejero","raw_affiliation_strings":["Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, E-46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0003-3681-7533","affiliations":[{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, E-46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074048649","display_name":"Marko Kosti\u0107","orcid":"https://orcid.org/0000-0002-0392-4976"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Marko Kosti\u0107","raw_affiliation_strings":["Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovi\u0107a 6, 21125 Novi Sad, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovi\u0107a 6, 21125 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067608137","display_name":"Marina Murillo\u2010Arcila","orcid":"https://orcid.org/0000-0001-6589-0452"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Marina Murillo-Arcila","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universitat Jaume I, Campus de R\u00edu Sec, E-12071 Castell\u00f3 de la Plana, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universitat Jaume I, Campus de R\u00edu Sec, E-12071 Castell\u00f3 de la Plana, Spain","institution_ids":["https://openalex.org/I10902133"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5079829006"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.189,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.86563936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"10","issue":"6","first_page":"211","last_page":"211"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9994000196456909,"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/T13234","display_name":"advanced mathematical theories","score":0.9894000291824341,"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":0.9879000186920166,"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/transitive-relation","display_name":"Transitive relation","score":0.7987476587295532},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7945064306259155},{"id":"https://openalex.org/keywords/topological-dynamics","display_name":"Topological dynamics","score":0.7033493518829346},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.5633563995361328},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.533625066280365},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5011248588562012},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4856654405593872},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.44924232363700867},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.43235525488853455},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.43038463592529297},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3280125558376312},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3187381625175476},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18204545974731445},{"id":"https://openalex.org/keywords/topological-tensor-product","display_name":"Topological tensor product","score":0.17708775401115417},{"id":"https://openalex.org/keywords/functional-analysis","display_name":"Functional analysis","score":0.06848976016044617}],"concepts":[{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.7987476587295532},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7945064306259155},{"id":"https://openalex.org/C47600822","wikidata":"https://www.wikidata.org/wiki/Q7825032","display_name":"Topological dynamics","level":5,"score":0.7033493518829346},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.5633563995361328},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.533625066280365},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5011248588562012},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4856654405593872},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.44924232363700867},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.43235525488853455},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.43038463592529297},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3280125558376312},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3187381625175476},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18204545974731445},{"id":"https://openalex.org/C178099376","wikidata":"https://www.wikidata.org/wiki/Q7825044","display_name":"Topological tensor product","level":4,"score":0.17708775401115417},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.06848976016044617},{"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/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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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":5,"locations":[{"id":"doi:10.3390/sym10060211","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10060211","pdf_url":"https://www.mdpi.com/2073-8994/10/6/211/pdf?version=1528706989","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:repositori.uji.es:10234/177069","is_oa":true,"landing_page_url":"http://hdl.handle.net/10234/177069","pdf_url":null,"source":{"id":"https://openalex.org/S4306400303","display_name":"Repositori UJI (Universitat Jaume I)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I10902133","host_organization_name":"Universitat Jaume I","host_organization_lineage":["https://openalex.org/I10902133"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:rodin.uca.es:10498/35392","is_oa":true,"landing_page_url":"http://hdl.handle.net/10498/35392","pdf_url":null,"source":{"id":"https://openalex.org/S4306400506","display_name":"RODIN (Universidad de C\u00e1diz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39147953","host_organization_name":"Universidad de C\u00e1diz","host_organization_lineage":["https://openalex.org/I39147953"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Symmetry, 10(6) (2018), 211","raw_type":"info:eu-repo/semantics/acceptedVersion"},{"id":"pmh:oai:doaj.org/article:f978812430fe411cbd82aabb32c878e6","is_oa":true,"landing_page_url":"https://doaj.org/article/f978812430fe411cbd82aabb32c878e6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 10, Iss 6, p 211 (2018)","raw_type":"article"},{"id":"pmh:oai:riunet.upv.es:10251/121833","is_oa":true,"landing_page_url":"https://riunet.upv.es/handle/10251/121833","pdf_url":null,"source":{"id":"https://openalex.org/S4306400639","display_name":"RiuNet (Universitat Polit\u00e8cnica de Val\u00e8ncia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.3390/sym10060211","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10060211","pdf_url":"https://www.mdpi.com/2073-8994/10/6/211/pdf?version=1528706989","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.4399999976158142,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G707173953","display_name":null,"funder_award_id":"MTM2016-75963-P","funder_id":"https://openalex.org/F4320321764","funder_display_name":"Ministerio de Educaci\u00f3n, Cultura y Deporte"}],"funders":[{"id":"https://openalex.org/F4320321764","display_name":"Ministerio de Educaci\u00f3n, Cultura y Deporte","ror":"https://ror.org/03nc27g21"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2807897117.pdf","grobid_xml":"https://content.openalex.org/works/W2807897117.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W96532434","https://openalex.org/W626893493","https://openalex.org/W1484040084","https://openalex.org/W1567268701","https://openalex.org/W1979332554","https://openalex.org/W1992908827","https://openalex.org/W2010598801","https://openalex.org/W2030867540","https://openalex.org/W2051638203","https://openalex.org/W2053622792","https://openalex.org/W2053833827","https://openalex.org/W2059735611","https://openalex.org/W2062233132","https://openalex.org/W2073540558","https://openalex.org/W2080021674","https://openalex.org/W2081657292","https://openalex.org/W2085006553","https://openalex.org/W2087900556","https://openalex.org/W2127930654","https://openalex.org/W2157737769","https://openalex.org/W2334477680","https://openalex.org/W2489691424","https://openalex.org/W2507368124","https://openalex.org/W2586490810","https://openalex.org/W2612978016","https://openalex.org/W2735751021","https://openalex.org/W2964177603","https://openalex.org/W4239398473","https://openalex.org/W4240509971","https://openalex.org/W4241627895","https://openalex.org/W4245909581"],"related_works":["https://openalex.org/W2295438979","https://openalex.org/W2056040336","https://openalex.org/W2383282217","https://openalex.org/W2388867275","https://openalex.org/W2354976030","https://openalex.org/W3121877141","https://openalex.org/W1968318401","https://openalex.org/W2349212754","https://openalex.org/W2888838995","https://openalex.org/W4406103934"],"abstract_inverted_index":{"The":[0,64],"existence":[1,77],"of":[2,7,26,42,66,72,78,91],"chaos":[3,37],"and":[4,35,48,62,74],"the":[5,24,39,76,89],"quest":[6],"dense":[8],"orbits":[9],"have":[10],"been":[11],"recently":[12],"considered":[13],"for":[14],"dynamical":[15],"systems":[16],"given":[17,87],"by":[18],"multivalued":[19],"linear":[20],"operators.":[21],"We":[22],"consider":[23],"notions":[25,68],"topological":[27,46],"transitivity,":[28],"topologically":[29],"mixing":[30],"property,":[31],"hypercyclicity,":[32],"periodic":[33],"points,":[34],"Devaney":[36],"in":[38,104],"general":[40],"case":[41],"binary":[43],"relations":[44,65],"on":[45],"spaces,":[47],"we":[49,96],"analyze":[50],"how":[51,99],"they":[52,57],"can":[53,101],"be":[54,102],"particularized":[55],"when":[56],"are":[58,81],"represented":[59],"with":[60,69,75],"graphs":[61],"digraphs.":[63],"these":[67],"different":[70],"types":[71],"connectivity":[73],"Hamiltonian":[79],"paths":[80],"also":[82,97],"exposed.":[83],"Special":[84],"attention":[85],"is":[86],"to":[88],"study":[90],"dynamics":[92],"over":[93],"tournaments.":[94],"Finally,":[95],"show":[98],"disjointness":[100],"introduced":[103],"this":[105],"setting.":[106]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}