The Khintchine constants for generalized continued fractions

Cited 2 time in webofscience Cited 0 time in scopus
  • Hit : 629
  • Download : 0
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.
Publisher
ELSEVIER SCIENCE INC
Issue Date
2003-12
Language
English
Article Type
Article
Citation

APPLIED MATHEMATICS AND COMPUTATION, v.144, pp.397 - 411

ISSN
0096-3003
URI
http://hdl.handle.net/10203/79076
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 2 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0