{"id":"https://openalex.org/W2152068564","doi":"https://doi.org/10.1155/2012/796180","title":"Iteration of Differentiable Functions under<i>m</i>-Modal Maps with Aperiodic Kneading Sequences","display_name":"Iteration of Differentiable Functions under<i>m</i>-Modal Maps with Aperiodic Kneading Sequences","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2152068564","doi":"https://doi.org/10.1155/2012/796180","mag":"2152068564"},"language":"en","primary_location":{"id":"doi:10.1155/2012/796180","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/796180","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/796180.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/796180.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073980643","display_name":"Maria F. Correia","orcid":"https://orcid.org/0000-0002-0363-2017"},"institutions":[{"id":"https://openalex.org/I21803372","display_name":"University of \u00c9vora","ror":"https://ror.org/02gyps716","country_code":"PT","type":"education","lineage":["https://openalex.org/I21803372"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Maria F. Correia","raw_affiliation_strings":["CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal","institution_ids":["https://openalex.org/I21803372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089078124","display_name":"C. Correia Ramos","orcid":"https://orcid.org/0000-0002-6772-7920"},"institutions":[{"id":"https://openalex.org/I21803372","display_name":"University of \u00c9vora","ror":"https://ror.org/02gyps716","country_code":"PT","type":"education","lineage":["https://openalex.org/I21803372"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Carlos C. Ramos","raw_affiliation_strings":["CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal","institution_ids":["https://openalex.org/I21803372"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039433721","display_name":"Sandra Vinagre","orcid":"https://orcid.org/0000-0002-0467-2256"},"institutions":[{"id":"https://openalex.org/I21803372","display_name":"University of \u00c9vora","ror":"https://ror.org/02gyps716","country_code":"PT","type":"education","lineage":["https://openalex.org/I21803372"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Sandra Vinagre","raw_affiliation_strings":["CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal","institution_ids":["https://openalex.org/I21803372"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073980643"],"corresponding_institution_ids":["https://openalex.org/I21803372"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.8384,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71603132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9959999918937683,"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":0.9959999918937683,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9728000164031982,"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/T10244","display_name":"Chaos control and synchronization","score":0.9714999794960022,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.9533663988113403},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8469212055206299},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7846739292144775},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6698572635650635},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5724522471427917},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.552990734577179},{"id":"https://openalex.org/keywords/iterated-function-system","display_name":"Iterated function system","score":0.5055770874023438},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4789453148841858},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4604215621948242},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.45161229372024536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3605877757072449},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3451080918312073},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.18378007411956787},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18262499570846558},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06139299273490906}],"concepts":[{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.9533663988113403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8469212055206299},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7846739292144775},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6698572635650635},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5724522471427917},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.552990734577179},{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.5055770874023438},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4789453148841858},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4604215621948242},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.45161229372024536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3605877757072449},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3451080918312073},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.18378007411956787},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18262499570846558},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06139299273490906},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/796180","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/796180","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/796180.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c48802d9b3594ea79bdf6c57b4096d50","is_oa":true,"landing_page_url":"https://doaj.org/article/c48802d9b3594ea79bdf6c57b4096d50","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"},{"id":"pmh:oai:dspace.uevora.pt:10174/5345","is_oa":false,"landing_page_url":"http://hdl.handle.net/10174/5345","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"},{"id":"pmh:oai:hindawi.com:10.1155/2012/796180","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/796180","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"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":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2012/796180","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/796180","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/796180.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2152068564.pdf","grobid_xml":"https://content.openalex.org/works/W2152068564.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W132845994","https://openalex.org/W320323277","https://openalex.org/W1537935065","https://openalex.org/W1994831302","https://openalex.org/W2025823532","https://openalex.org/W2035236867","https://openalex.org/W2049466345","https://openalex.org/W2090648759","https://openalex.org/W2267658675","https://openalex.org/W2316409338","https://openalex.org/W2477084700"],"related_works":["https://openalex.org/W1561687547","https://openalex.org/W2369480152","https://openalex.org/W4287710035","https://openalex.org/W2017482687","https://openalex.org/W2368621955","https://openalex.org/W2972725323","https://openalex.org/W3158017144","https://openalex.org/W2068677575","https://openalex.org/W2356012241","https://openalex.org/W2082089484"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,22,44,52,56,65,70,73,78],"dynamical":[3],"system":[4],"(,":[5],"),":[6],"where":[7,25],"is":[8,21,26],"a":[9,27],"class":[10],"of":[11,46,48,51,59,72,77],"differentiable":[12,28],"functions":[13,54],"defined":[14],"on":[15],"some":[16,37],"interval":[17],"and":[18,39],":":[19],"\u2192":[20],"operator":[23],",":[24],"m":[29],"-modal":[30],"map.":[31],"Using":[32],"an":[33],"algorithm,":[34],"we":[35,63],"obtained":[36],"numerical":[38],"symbolic":[40],"results":[41],"related":[42],"to":[43],"frequencies":[45],"occurrence":[47],"critical":[49,75],"values":[50,76],"iterated":[53,79],"when":[55],"kneading":[57],"sequences":[58],"are":[60],"aperiodic.":[61],"Moreover,":[62],"analyze":[64],"evolution":[66],"as":[67,69],"well":[68],"distribution":[71],"aperiodic":[74],"functions.":[80]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2016-06-24T00:00:00"}