Metrical Theory of Continued Fractions

Metrical Theory of Continued Fractions
Author :
Publisher : Springer Science & Business Media
Total Pages : 397
Release :
ISBN-10 : 9789401599405
ISBN-13 : 9401599408
Rating : 4/5 (408 Downloads)

Book Synopsis Metrical Theory of Continued Fractions by : M. Iosifescu

Download or read book Metrical Theory of Continued Fractions written by M. Iosifescu and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real numbers. We have attempted to give the best possible results known so far, with proofs which are the simplest and most direct. The book has had a long gestation period because we first decided to write it in March 1994. This gave us the possibility of essentially improving the initial versions of many parts of it. Even if the two authors are different in style and approach, every effort has been made to hide the differences. Let 0 denote the set of irrationals in I = [0,1]. Define the (reg ular) continued fraction transformation T by T (w) = fractional part of n 1/w, w E O. Write T for the nth iterate of T, n E N = {O, 1, ... }, n 1 with TO = identity map. The positive integers an(w) = al(T - (W)), n E N+ = {1,2··· }, where al(w) = integer part of 1/w, w E 0, are called the (regular continued fraction) digits of w. Writing . for arbitrary indeterminates Xi, 1 :::; i :::; n, we have w = lim [al(w),··· , an(w)], w E 0, n--->oo thus explaining the name of T. The above equation will be also written as w = lim [al(w), a2(w),···], w E O.


Metrical Theory of Continued Fractions Related Books

Metrical Theory of Continued Fractions
Language: en
Pages: 397
Authors: M. Iosifescu
Categories: Mathematics
Type: BOOK - Published: 2013-06-29 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real
Metrical Theory of Continued Fractions
Language: en
Pages: 408
Authors: M. Iosifescu
Categories: Mathematics
Type: BOOK - Published: 2002-09-30 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The book is essentially based on recent work of the authors. In order to unify and generalize the results obtained so far, new concepts have been introduced, e.
Continued Fractions
Language: en
Pages: 200
Authors: Andrew M Rockett
Categories: Mathematics
Type: BOOK - Published: 1992-08-08 - Publisher: World Scientific Publishing Company

DOWNLOAD EBOOK

This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of th
Metrical Theory of Continued Fractions
Language: en
Pages: 383
Authors: M. Iosifescu
Categories: Mathematics
Type: BOOK - Published: 2014-03-14 - Publisher: Springer

DOWNLOAD EBOOK

This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real
Continued Fractions
Language: en
Pages: 261
Authors: Doug Hensley
Categories: Mathematics
Type: BOOK - Published: 2006-03-01 - Publisher: World Scientific

DOWNLOAD EBOOK

The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Le