{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T01:12:20Z","timestamp":1649207540253},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> For a class of sets defined in terms of frequencies of digits in some integer base m, we study their Hausdorff dimension. Our main aim is to consider nonlinear perturbations of the case when all frequencies are equal (and thus when the Hausdorff dimension is maximal). As a first step we consider the case when only one frequency is related to another, by the function x \u21a6 1\/m + \u03b5x + \u03b4x<jats:sup>2<\/jats:sup>, and for which the computations are already quite substantial. We show that the Hausdorff dimension is analytic in the parameters \u03b5 and \u03b4, and we estimate the asymptotic behavior of the Taylor coefficients of the dimension in terms of m. <\/jats:p>","DOI":"10.1142\/s1230161212500187","type":"journal-article","created":{"date-parts":[[2012,9,21]],"date-time":"2012-09-21T08:00:39Z","timestamp":1348214439000},"page":"1250018","source":"Crossref","is-referenced-by-count":0,"title":["Hausdorff Dimension and Nonlinear Relations Between Frequencies of Digits"],"prefix":"10.1142","volume":"19","author":[{"given":"Luis","family":"Barreira","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade T\u00e9cnica de Lisboa, 1049\u2013001 Lisboa, Portugal"}]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade T\u00e9cnica de Lisboa, 1049\u2013001 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2012,9,21]]},"reference":[{"key":"rf1","series-title":"Progress in Mathematics","volume-title":"Dimension and Recurrence in Hyperbolic Dynamics","volume":"272","author":"Barreira L.","year":"2008"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0206-2"},{"key":"rf3","first-page":"413","volume":"97","author":"Barreira L.","journal-title":"J. Number Theory"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(01)01228-4"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01448030"},{"key":"rf6","volume-title":"Ergodic Theory and Information","author":"Billingsley P.","year":"1965"},{"key":"rf7","first-page":"31","volume":"20","author":"Eggleston H.","journal-title":"Quart. J. Math. Oxford Ser."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/S0024610701002137"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.7208\/chicago\/9780226662237.001.0001"},{"key":"rf10","first-page":"317","volume":"23","author":"Takens F.","journal-title":"Ergodic Theory Dynam. Syst."}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161212500187","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T18:16:53Z","timestamp":1565201813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1230161212500187"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":10,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,9,21]]},"published-print":{"date-parts":[[2012,9]]}},"alternative-id":["10.1142\/S1230161212500187"],"URL":"https:\/\/doi.org\/10.1142\/s1230161212500187","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}