{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T18:12:16Z","timestamp":1648577536578},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>Let F<jats:sub>a,\u03bb<\/jats:sub>be the Blaschke product of the form F<jats:sub>a,\u03bb<\/jats:sub>= \u03bbz<jats:sup>2<\/jats:sup>((z - a)\/(1 - \u0101z)) and \u03b1 denote an irrational number satisfying the Brjuno condition. Henriksen [1997] showed that for any \u03b1 there exists a constant a<jats:sub>0<\/jats:sub>\u2267 3 and a continuous function \u03bb(a) such that F<jats:sub>a,\u03bb(a)<\/jats:sub>possesses an Herman ring and also that modulus M(a) of the Herman ring approaches 0 as a approaches a<jats:sub>0<\/jats:sub>. It is remarked that the question whether a<jats:sub>0<\/jats:sub>= 3 holds or not is open. According to the idea of Fagella and Geyer [2003] we can show that for a certain set of irrational rotation numbers, a<jats:sub>0<\/jats:sub>is strictly larger than 3.<\/jats:p>","DOI":"10.1142\/s0218127409023007","type":"journal-article","created":{"date-parts":[[2009,3,20]],"date-time":"2009-03-20T10:36:08Z","timestamp":1237545368000},"page":"445-451","source":"Crossref","is-referenced-by-count":0,"title":["HERMAN RINGS OF BLASCHKE PRODUCTS OF DEGREE 3"],"prefix":"10.1142","volume":"19","author":[{"given":"YOSHIHISA","family":"FUJIMOTO","sequence":"first","affiliation":[{"name":"School of Business and Administration, Meiji University, 1-9-1 Eifuku, Suginamiku, Tokyo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1090\/trans2\/046\/11","volume":"46","author":"Arnold V. I.","journal-title":"Transl. Amer. Math. Soc., 2nd Series"},{"key":"rf2","first-page":"131","volume":"25","author":"Brjuno A. D.","journal-title":"Trans. Moscow Math. Soc."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610705007015"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-78043-1"},{"key":"rf5","first-page":"151","author":"Douady A.","journal-title":"Seminar Bourbaki, Ast\u00e9risque"},{"key":"rf6","first-page":"493","volume":"23","author":"Fagella N.","journal-title":"Erg. Th. Dyn. Syst."},{"key":"rf9","volume-title":"Dynamics in One Complex Variable","author":"Milnor J.","year":"2006"},{"key":"rf10","first-page":"273","volume":"206","author":"P\u00e9rez-Marco R.","journal-title":"Ast\u00e9risque"},{"key":"rf11","first-page":"1","volume":"20","author":"Shishikura M.","journal-title":"Ann. Sci. \u00c9cole Norm. Sup. 4\u00e9me S\u00e9ries t."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409023007","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T00:18:48Z","timestamp":1589674728000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409023007"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1142\/S0218127409023007"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409023007","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}