{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,25]],"date-time":"2024-06-25T05:56:56Z","timestamp":1719295016974},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,7]]},"abstract":"<jats:p> Given a family of bimodal maps on the interval, we need to consider a second topological invariant, other than the usual topological entropy, in order to classify it. With this work, we want to understand how to use this second invariant to distinguish bimodal maps with the same topological entropy and, in particular, how this second invariant changes within a given type of topological entropy level set. In order to do that, we use the kneading theory framework and introduce a symbolic product * between kneading invariants of maps from the same topological entropy level set, for which we show that the second invariant is preserved. Finally, we also show that the change of the second invariant follows closely the symbolic order between bimodal kneading sequences. <\/jats:p>","DOI":"10.1142\/s0218127403007552","type":"journal-article","created":{"date-parts":[[2003,8,28]],"date-time":"2003-08-28T09:49:31Z","timestamp":1062064171000},"page":"1701-1709","source":"Crossref","is-referenced-by-count":8,"title":["Isentropic Real Cubic Maps"],"prefix":"10.1142","volume":"13","author":[{"given":"Nuno","family":"Martins","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Braga, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo","family":"Severino","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade do Minho, Braga, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Sousa Ramos","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade do Minho, Braga, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","author":"Douady A.","journal-title":"Plub. Mat. d'Orsay"},{"key":"rf3","unstructured":"A.\u00a0Douady, Real and Complex Dynamical Systems, eds. B.\u00a0Branner and P.\u00a0Hjorth (Kluwer, Dordrecht, 1995)\u00a0pp. 1\u20138."},{"key":"rf4","first-page":"173","volume":"70","author":"Guckenheimer J.","journal-title":"Commun. Math. Phys."},{"key":"rf5","first-page":"193","volume":"13","author":"Lampreia J. P.","journal-title":"Annales Mathematicae Silesianae"},{"key":"rf6","first-page":"164","volume":"37","author":"MacKay R.","journal-title":"J. London Math. Soc."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/s002200050018"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/0143033"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007552","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:16:31Z","timestamp":1565136991000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7]]},"references-count":7,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,7]]}},"alternative-id":["10.1142\/S0218127403007552"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007552","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,7]]}}}