{"id":"https://openalex.org/W3017811005","doi":"https://doi.org/10.1155/2020/1853467","title":"Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions","display_name":"Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions","publication_year":2020,"publication_date":"2020-04-23","ids":{"openalex":"https://openalex.org/W3017811005","doi":"https://doi.org/10.1155/2020/1853467","mag":"3017811005"},"language":"lv","primary_location":{"id":"doi:10.1155/2020/1853467","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/1853467","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2020/1853467.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/2020/1853467.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014414437","display_name":"Kasey Bray","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kasey Bray","raw_affiliation_strings":["Montgomery Bell Academy, Nashville, TN 37205, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Montgomery Bell Academy, Nashville, TN 37205, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110048399","display_name":"Jerry Dwyer","orcid":null},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jerry Dwyer","raw_affiliation_strings":["Texas Tech University, Lubbock, TX 79409, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas Tech University, Lubbock, TX 79409, USA","institution_ids":["https://openalex.org/I12315562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024937255","display_name":"Roger Barnard","orcid":"https://orcid.org/0000-0002-0538-7158"},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roger W. Barnard","raw_affiliation_strings":["Texas Tech University, Lubbock, TX 79409, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas Tech University, Lubbock, TX 79409, USA","institution_ids":["https://openalex.org/I12315562"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089037263","display_name":"G. Brock Williams","orcid":"https://orcid.org/0000-0002-9199-7111"},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"G. Brock Williams","raw_affiliation_strings":["Texas Tech University, Lubbock, TX 79409, USA"],"raw_orcid":"https://orcid.org/0000-0002-9199-7111","affiliations":[{"raw_affiliation_string":"Texas Tech University, Lubbock, TX 79409, USA","institution_ids":["https://openalex.org/I12315562"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089037263"],"corresponding_institution_ids":["https://openalex.org/I12315562"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.784,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65716642,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"10"},"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/T10244","display_name":"Chaos control and synchronization","score":0.9801999926567078,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9560999870300293,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5860023498535156},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3576192259788513},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34342968463897705}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5860023498535156},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3576192259788513},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34342968463897705}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2020/1853467","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/1853467","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2020/1853467.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:RePEc:hin:jijmms:1853467","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2020/1853467.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:ea08fd18aa884ab3b6fd8bc5a089ea48","is_oa":true,"landing_page_url":"https://doaj.org/article/ea08fd18aa884ab3b6fd8bc5a089ea48","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 2020 (2020)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2020/1853467","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/1853467","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"},{"id":"pmh:oai:ttu-ir.tdl.org:2346/95671","is_oa":true,"landing_page_url":"https://hdl.handle.net/2346/95671","pdf_url":null,"source":{"id":"https://openalex.org/S4306402519","display_name":"ThinkTech (Texas Tech University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I12315562","host_organization_name":"Texas Tech University","host_organization_lineage":["https://openalex.org/I12315562"],"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":"Article"}],"best_oa_location":{"id":"doi:10.1155/2020/1853467","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/1853467","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2020/1853467.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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1545346317","https://openalex.org/W1700084322","https://openalex.org/W2046151982","https://openalex.org/W2902913510"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"The":[0,46],"dynamical":[1],"systems":[2],"of":[3,38,48,71,84,92],"trigonometric":[4],"functions":[5],"are":[6,60,65],"explored,":[7],"with":[8],"a":[9],"focus":[10],"on":[11],"<mml:math":[12,32,39,53,76,80],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[13,33,40,54,77,81],"id=\"M1\"><mml:mrow><mml:mi>t</mml:mi><mml:mfenced":[14],"open=\"(\"":[15,19,35,43,57],"close=\")\"":[16,20,36,44,58],"separators=\"|\"><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mi":[17],"mathvariant=\"normal\">tan</mml:mi><mml:mfenced":[18],"separators=\"|\"><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math>":[21,59],"and":[22,62,79,88],"the":[23,29,68,85,90,93],"fractal":[24,94],"image":[25],"created":[26,50],"by":[27],"iterating":[28,52],"Newton":[30,86],"map,":[31],"id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mfenced":[34],"separators=\"|\"><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math>,":[37],"id=\"M3\"><mml:mrow><mml:mo>":[41],"</mml:mo><mml:mi>t</mml:mi><mml:mfenced":[42],"separators=\"|\"><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math>.":[45],"basins":[47,70],"attraction":[49],"from":[51],"id=\"M4\"><mml:mrow><mml:mo>":[55],"</mml:mo><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mfenced":[56],"analyzed,":[61],"some":[63],"bounds":[64],"determined":[66],"for":[67],"primary":[69],"attraction.":[72],"We":[73],"further":[74],"prove":[75],"id=\"M5\"><mml:mi>x</mml:mi></mml:math>-":[78],"id=\"M6\"><mml:mi>y</mml:mi></mml:math>-axis":[82],"symmetry":[83],"map":[87],"explore":[89],"nature":[91],"images.":[95]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}