DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choe, Geon Ho | ko |
dc.contributor.author | Kim, C | ko |
dc.date.accessioned | 2013-03-03T14:27:48Z | - |
dc.date.available | 2013-03-03T14:27:48Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 2003-12 | - |
dc.identifier.citation | APPLIED MATHEMATICS AND COMPUTATION, v.144, pp.397 - 411 | - |
dc.identifier.issn | 0096-3003 | - |
dc.identifier.uri | http://hdl.handle.net/10203/79076 | - |
dc.description.abstract | Let T-p(x) - 1/x(p) (mod 1) for 0 < x < 1 and T-p(0) = 0. It is known that if p > p(0) = 0.241485.... then there exists an ergodic invariant measure of the form rho(p)dx. Let a(n) = [(1/T-p(n-1)(x))(p)], n greater than or equal to 1, where [t] is the integer part of t. If p = 1, then a(1), a(2),...,a(n) are the partial quotients of the classical continued fraction of x. For a real number q, we consider averages of a(n): [GRAPHICS] We show that (i) for almost every x, K-p,K-q : = lim(n-->infinity)K (p, q, n, x) < &INFIN; if and only if q < 1/p, (ii) lim(p-->infinity) (log K-p,K-q)/p = 1 if q = 0 where log denotes the natural logarithm, (iii) lim(p-->infinity) log K-p,K-q/ log p = 1 /\q\ if q < 0. The limiting behavior of K-p,K-q is investigated as p &DARR; p(o) with computer simulations. (C) 2002 Elsevier Inc. All rights reserved. | - |
dc.language | English | - |
dc.publisher | ELSEVIER SCIENCE INC | - |
dc.title | The Khintchine constants for generalized continued fractions | - |
dc.type | Article | - |
dc.identifier.wosid | 000184353800016 | - |
dc.identifier.scopusid | 2-s2.0-0038451466 | - |
dc.type.rims | ART | - |
dc.citation.volume | 144 | - |
dc.citation.beginningpage | 397 | - |
dc.citation.endingpage | 411 | - |
dc.citation.publicationname | APPLIED MATHEMATICS AND COMPUTATION | - |
dc.contributor.localauthor | Choe, Geon Ho | - |
dc.contributor.nonIdAuthor | Kim, C | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Khintchine constant | - |
dc.subject.keywordAuthor | continued fraction | - |
dc.subject.keywordAuthor | Lyapunov exponent | - |
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