DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choe, Geon Ho | ko |
dc.contributor.author | Seo, BK | ko |
dc.date.accessioned | 2013-03-04T07:20:17Z | - |
dc.date.available | 2013-03-04T07:20:17Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 2001-09 | - |
dc.identifier.citation | PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, v.77, no.7, pp.134 - 137 | - |
dc.identifier.issn | 0386-2194 | - |
dc.identifier.uri | http://hdl.handle.net/10203/81973 | - |
dc.description.abstract | Let 0 < <theta> < 1 be irrational and T(<theta>)x = x + theta mod 1 on (0, 1). Consider the partition Q(n) = {((i-1)/2(n), i/2(n)) : 1 less than or equal to i less than or equal to 2(n)} and let Q(n)(x) denote the interval in Q(n) containing x. Define two versions of the first return time: J(n)(x) = min{j greater than or equal to 1 : parallel tox - T(theta)(j)x parallel to = parallel toj . theta parallel to < 1/2(n)} where <parallel>t parallel to = min(n is an element ofZ) vertical bart -n vertical bar, and K-n(x) = min{j greater than or equal to 1 : T-theta(j) x is an element of Q(n)(x)}. We show that log J(n)/n --> 1 and log K-n(x)/n --> 1 a.e. as n --> infinity for a.e. theta. | - |
dc.language | English | - |
dc.publisher | JAPAN ACAD | - |
dc.title | Recurrence speed of multiples of an irrational number | - |
dc.type | Article | - |
dc.identifier.wosid | 000171637200010 | - |
dc.identifier.scopusid | 2-s2.0-23044531324 | - |
dc.type.rims | ART | - |
dc.citation.volume | 77 | - |
dc.citation.issue | 7 | - |
dc.citation.beginningpage | 134 | - |
dc.citation.endingpage | 137 | - |
dc.citation.publicationname | PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | - |
dc.contributor.localauthor | Choe, Geon Ho | - |
dc.contributor.nonIdAuthor | Seo, BK | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | recurrence time | - |
dc.subject.keywordAuthor | irrational translation | - |
dc.subject.keywordAuthor | continued fractions | - |
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