Metrical Theory Of Continued Fractions PDF Download
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Author | : M. Iosifescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 397 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 9401599408 |
Download Metrical Theory of Continued Fractions Book in PDF, ePub and Kindle
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.
Author | : M. Iosifescu |
Publisher | : Springer |
Total Pages | : 383 |
Release | : 2014-03-14 |
Genre | : Mathematics |
ISBN | : 9789401599412 |
Download Metrical Theory of Continued Fractions Book in PDF, ePub and Kindle
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.
Author | : A. M. Rockett |
Publisher | : World Scientific |
Total Pages | : 202 |
Release | : 1992-08-01 |
Genre | : Mathematics |
ISBN | : 9789810210526 |
Download Continued Fractions Book in PDF, ePub and Kindle
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 the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.
Author | : Andrew Mansfield Rockett |
Publisher | : |
Total Pages | : 72 |
Release | : 1977 |
Genre | : Continued fractions |
ISBN | : |
Download The Metrical Theory of Continued Fractions to the Nearest Integer Book in PDF, ePub and Kindle
Author | : Wieb Bosma |
Publisher | : |
Total Pages | : 15 |
Release | : 1987 |
Genre | : |
ISBN | : |
Download Metrical Theory for Optimal Continued Fractions Book in PDF, ePub and Kindle
Author | : Andrew Mansfield Rockett |
Publisher | : |
Total Pages | : |
Release | : 1992 |
Genre | : |
ISBN | : 9789814439787 |
Download Continued Fractions Book in PDF, ePub and Kindle
Author | : Marius Iosifescu |
Publisher | : |
Total Pages | : 143 |
Release | : 2011 |
Genre | : |
ISBN | : 9789732720493 |
Download Metrical Theory of Some Continued Fraction Expansions Book in PDF, ePub and Kindle
Author | : Aleksandr I?Akovlevich Khinchin |
Publisher | : Courier Corporation |
Total Pages | : 116 |
Release | : 1997-05-14 |
Genre | : Mathematics |
ISBN | : 9780486696300 |
Download Continued Fractions Book in PDF, ePub and Kindle
Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. 1964 edition. Prefaces.
Author | : Doug Hensley |
Publisher | : World Scientific |
Total Pages | : 261 |
Release | : 2006-03-01 |
Genre | : Mathematics |
ISBN | : 9814479438 |
Download Continued Fractions Book in PDF, ePub and Kindle
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 Legendre. While our understanding of continued fractions and related methods for simultaneous diophantine approximation has burgeoned over the course of the past decade and more, many of the results have not been brought together in book form. Continued fractions have been studied from the perspective of number theory, complex analysis, ergodic theory, dynamic processes, analysis of algorithms, and even theoretical physics, which has further complicated the situation.This book places special emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. Extensive, attractive computer-generated graphics are presented, and the underlying algorithms are discussed and made available.
Author | : Andrew M Rockett |
Publisher | : World Scientific Publishing Company |
Total Pages | : 200 |
Release | : 1992-08-08 |
Genre | : Mathematics |
ISBN | : 9813103418 |
Download Continued Fractions Book in PDF, ePub and Kindle
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 the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.