{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T23:55:58Z","timestamp":1648857358379},"reference-count":12,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>We consider the dynamical system (, ), where is a class of differentiable functions defined on some interval and : \u2192 is the operator , where is a differentiable<jats:italic>m<\/jats:italic>-modal map. Using an algorithm, we obtained some numerical and symbolic results related to the frequencies of occurrence of critical values of the iterated functions when the kneading sequences of are aperiodic. Moreover, we analyze the evolution as well as the distribution of the aperiodic critical values of the iterated functions.<\/jats:p>","DOI":"10.1155\/2012\/796180","type":"journal-article","created":{"date-parts":[[2012,8,8]],"date-time":"2012-08-08T21:09:25Z","timestamp":1344460165000},"page":"1-17","source":"Crossref","is-referenced-by-count":1,"title":["Iteration of Differentiable Functions under<i>m<\/i>-Modal Maps with Aperiodic Kneading Sequences"],"prefix":"10.1155","volume":"2012","author":[{"given":"Maria F.","family":"Correia","sequence":"first","affiliation":[{"name":"CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal"}]},{"given":"Carlos C.","family":"Ramos","sequence":"additional","affiliation":[{"name":"CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal"}]},{"given":"Sandra","family":"Vinagre","sequence":"additional","affiliation":[{"name":"CIMA-UE and Department of Mathematics, University of \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal"}]}],"member":"98","reference":[{"key":"8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499000900"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-1763-0"},{"key":"10","first-page":"393","volume":"346","year":"2004","journal-title":"Grazer Mathematische Berichte"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-006-1942-4"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.043"},{"key":"4"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082847"},{"issue":"1","key":"6","doi-asserted-by":"crossref","first-page":"45","DOI":"10.4064\/sm-67-1-45-63","volume":"67","year":"1980","journal-title":"Studia Mathematica"},{"key":"1","volume-title":"Symbolic dynamics for iterated smooth functions","volume":"354","year":"2009"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1142\/9789814287654_0016"},{"issue":"2","key":"3","first-page":"151","volume":"70","year":"2011","journal-title":"International Journal of Pure and Applied Mathematics"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01982351"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/796180.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/796180.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/796180.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,2]],"date-time":"2019-07-02T17:19:59Z","timestamp":1562087999000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2012\/796180\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":12,"alternative-id":["796180","796180"],"URL":"https:\/\/doi.org\/10.1155\/2012\/796180","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}