{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T18:54:49Z","timestamp":1649184889280},"reference-count":15,"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> We consider those linear mod one transformations f<jats:sub>\u03b2,\u03b1<\/jats:sub> on the unit interval, for which the respective kneading sequences are periodic. Then, we construct the corresponding Markov transition matrices A<jats:sub>\u03b2,\u03b1<\/jats:sub>. Using symbolic dynamics techniques, we prove that the Bowen\u2013Franks groups BF(A<jats:sub>\u03b2,\u03b1<\/jats:sub>) can be directly computed from the number of symbols of the respective periodic words of the kneading sequences of f<jats:sub>\u03b2,\u03b1<\/jats:sub>. <\/jats:p>","DOI":"10.1142\/s0218127403007837","type":"journal-article","created":{"date-parts":[[2003,8,28]],"date-time":"2003-08-28T09:49:31Z","timestamp":1062064171000},"page":"1997-2004","source":"Crossref","is-referenced-by-count":1,"title":["Bowen\u2013Franks Groups Associated with Linear Mod One Transformations"],"prefix":"10.1142","volume":"13","author":[{"given":"Nuno","family":"Martins","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Av. Rovisco Pais, 1049-001 Lisboa Codex, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Sousa Ramos","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Av. Rovisco Pais, 1049-001 Lisboa Codex, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2307\/1971159"},{"key":"rf2","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1017\/S0143385700008920","volume":"16","author":"Flatto L.","journal-title":"Ergod. Th. Dyn. Syst."},{"key":"rf3","first-page":"307","volume":"50","author":"Guckenheimer J.","journal-title":"Inst. Hautes Etudes Sci. Publ. Math."},{"key":"rf4","first-page":"92","volume":"23","author":"Hofbauer F.","journal-title":"J. London Math. Soc."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385798108350"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127493001276"},{"key":"rf7","first-page":"1","volume":"54","author":"Lampreia J. P.","journal-title":"Portugaliae Math."},{"key":"rf8","volume-title":"Algebra","author":"Lang S.","year":"1965"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626302"},{"key":"rf11","first-page":"1831","volume":"21","author":"Matsumoto K.","journal-title":"Ergod. Th. Dyn. Syst."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01897025"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(75)90012-9"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.1998.4.475"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.2307\/1970908"},{"key":"rf16","first-page":"321","volume":"50","author":"Williams R. F.","journal-title":"Inst. Hautes Etudes Sci. Publ. Math."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007837","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:17:24Z","timestamp":1565137044000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007837"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7]]},"references-count":15,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,7]]}},"alternative-id":["10.1142\/S0218127403007837"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007837","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,7]]}}}