{"id":"https://openalex.org/W2517745410","doi":"https://doi.org/10.1142/s0218127416501509","title":"Invariant Sets for Monotone Local Dendrite Maps","display_name":"Invariant Sets for Monotone Local Dendrite Maps","publication_year":2016,"publication_date":"2016-08-01","ids":{"openalex":"https://openalex.org/W2517745410","doi":"https://doi.org/10.1142/s0218127416501509","mag":"2517745410"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416501509","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501509","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/A5077474891","display_name":"Hafedh Abdelli","orcid":"https://orcid.org/0000-0003-1157-9655"},"institutions":[{"id":"https://openalex.org/I179097149","display_name":"University of Carthage","ror":"https://ror.org/057x6za15","country_code":"TN","type":"education","lineage":["https://openalex.org/I179097149"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Hafedh Abdelli","raw_affiliation_strings":["Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Jarzouna 7021, Tunisia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Jarzouna 7021, Tunisia","institution_ids":["https://openalex.org/I179097149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039431953","display_name":"Habib Marzougui","orcid":null},"institutions":[{"id":"https://openalex.org/I179097149","display_name":"University of Carthage","ror":"https://ror.org/057x6za15","country_code":"TN","type":"education","lineage":["https://openalex.org/I179097149"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Habib Marzougui","raw_affiliation_strings":["Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Jarzouna 7021, Tunisia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Jarzouna 7021, Tunisia","institution_ids":["https://openalex.org/I179097149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077474891"],"corresponding_institution_ids":["https://openalex.org/I179097149"],"apc_list":null,"apc_paid":null,"fwci":1.1008,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.76538273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"09","first_page":"1650150","last_page":"1650150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9998999834060669,"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":0.9998999834060669,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematics","display_name":"Mathematics","score":0.6820670366287231},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5705140829086304},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5260705351829529},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.46460670232772827},{"id":"https://openalex.org/keywords/irrational-number","display_name":"Irrational number","score":0.42893919348716736},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17254340648651123},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10616692900657654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6820670366287231},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5705140829086304},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5260705351829529},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.46460670232772827},{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.42893919348716736},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17254340648651123},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10616692900657654}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416501509","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501509","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1517662484","https://openalex.org/W1569683457","https://openalex.org/W1855277279","https://openalex.org/W1975123057","https://openalex.org/W1983722259","https://openalex.org/W2017862174","https://openalex.org/W2024675730","https://openalex.org/W2026500717","https://openalex.org/W2065865013","https://openalex.org/W2135843380","https://openalex.org/W2167662605","https://openalex.org/W4253125818"],"related_works":["https://openalex.org/W3088646517","https://openalex.org/W2973552040","https://openalex.org/W2185277279","https://openalex.org/W4220768180","https://openalex.org/W2377639682","https://openalex.org/W2792087242","https://openalex.org/W2387799803","https://openalex.org/W3100817393","https://openalex.org/W3120892761","https://openalex.org/W2797611542"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,10,19,28,43,50,55,62,69,88,95,106,113,127,137,152,157],"see":[2,11,20,23,26,29,44,51,56,63,70,74,89,96,100,107,114,128,138,153,158],"text]":[3,12,30,45,64,75,90,101,108,115,139,159],"be":[4,13],"a":[5,14,84,110],"local":[6],"dendrite":[7],"and":[8,42,77,103,112],"let":[9],"monotone":[15],"map.":[16],"Denote":[17],"by":[18],"text],":[21,24,27],"RR[Formula:":[22],"UR[Formula:":[25],"the":[31,46,124,131,148,165],"set":[32],"of":[33,48,54,123,150,156],"periodic":[34,85],"(resp.,":[35],"regularly":[36],"recurrent,":[37,39],"uniformly":[38],"recurrent)":[40],"points":[41],"union":[47],"all":[49,151],"text]-limit":[52,154],"sets":[53,155],"text].":[57,71,97,129],"We":[58],"show":[59,146],"that":[60,136,147],"if":[61,76,79,102,105],"is":[65,83,91,109,116,160],"nonempty,":[66],"then":[67,93],"(i)":[68],"(ii)":[72],"R[Formula:":[73,99],"only":[78,104],"every":[80],"cut":[81],"point":[82],"point.":[86],"If":[87],"empty,":[92],"(iii)":[94],"(iv)":[98],"circle":[111,126],"topologically":[117],"conjugate":[118],"to":[119,164],"an":[120],"irrational":[121],"rotation":[122],"unit":[125],"On":[130],"other":[132],"hand,":[133],"we":[134,145],"prove":[135],"has":[140],"no":[141],"Li\u2013Yorke":[142],"pair.":[143],"Moreover,":[144],"family":[149],"closed":[161],"with":[162],"respect":[163],"Hausdorff":[166],"metric.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}