{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:37:38Z","timestamp":1747190258513,"version":"3.40.5"},"reference-count":7,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T00:00:00Z","timestamp":1587600000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2020,4,23]]},"abstract":"<jats:p>The dynamical systems of trigonometric functions are explored, with a focus on <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>t<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>=<\/mml:mo><mml:mi mathvariant=\"normal\">tan<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math> and the fractal image created by iterating the Newton map, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" 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 open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>, of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mo>\u2009<\/mml:mo><mml:mi>t<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>. The basins of attraction created from iterating <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mo>\u2009<\/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 open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math> are analyzed, and some bounds are determined for the primary basins of attraction. We further prove <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>x<\/mml:mi><\/mml:math>- and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>y<\/mml:mi><\/mml:math>-axis symmetry of the Newton map and explore the nature of the fractal images.<\/jats:p>","DOI":"10.1155\/2020\/1853467","type":"journal-article","created":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T23:33:01Z","timestamp":1587684781000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions"],"prefix":"10.1155","volume":"2020","author":[{"given":"Kasey","family":"Bray","sequence":"first","affiliation":[{"name":"Montgomery Bell Academy, Nashville, TN 37205, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jerry","family":"Dwyer","sequence":"additional","affiliation":[{"name":"Texas Tech University, Lubbock, TX 79409, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roger W.","family":"Barnard","sequence":"additional","affiliation":[{"name":"Texas Tech University, Lubbock, TX 79409, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9199-7111","authenticated-orcid":true,"given":"G. Brock","family":"Williams","sequence":"additional","affiliation":[{"name":"Texas Tech University, Lubbock, TX 79409, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","first-page":"9","volume":"23","year":"2009","journal-title":"Australian Senior Mathematics Journal"},{"key":"2","doi-asserted-by":"crossref","first-page":"1666","DOI":"10.1080\/17476933.2018.1547285","volume":"64","year":"2019","journal-title":"Complex Variables and Elliptic Equations"},{"year":"2009","key":"3"},{"year":"2012","key":"4"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1090\/s0002-9939-07-09015-6"},{"key":"6","first-page":"125","volume-title":"Complex exponential dynamics","volume":"3","year":"2010"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1090\/s1088-4173-97-00017-9"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/1853467.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/1853467.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/1853467.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T23:33:04Z","timestamp":1587684784000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2020\/1853467\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,23]]},"references-count":7,"alternative-id":["1853467","1853467"],"URL":"https:\/\/doi.org\/10.1155\/2020\/1853467","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2020,4,23]]}}}