Metrical Theory Of Continued Fractions
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Metrical Theory Of Continued Fractions
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Author : M. Iosifescu
language : en
Publisher: Springer
Release Date : 2014-03-14
Metrical Theory Of Continued Fractions written by M. Iosifescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-14 with Mathematics categories.
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
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Author : M. Iosifescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Metrical Theory Of Continued Fractions written by M. Iosifescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Continued Fractions
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Author : A. M. Rockett
language : en
Publisher: World Scientific
Release Date : 1992-08-01
Continued Fractions written by A. M. Rockett and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-01 with Mathematics categories.
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.
Continued Fractions
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Author : Andrew Mansfield Rockett
language : en
Publisher:
Release Date : 1992
Continued Fractions written by Andrew Mansfield Rockett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Metrical Theory Of Some Continued Fraction Expansions
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Author : Marius Iosifescu
language : en
Publisher:
Release Date : 2011
Metrical Theory Of Some Continued Fraction Expansions written by Marius Iosifescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Analytic Theory Of Continued Fractions
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Author : Hubert Stanley Wall
language : en
Publisher: Courier Dover Publications
Release Date : 2018-05-16
Analytic Theory Of Continued Fractions written by Hubert Stanley Wall and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-16 with Mathematics categories.
One of the most authoritative and comprehensive books on continued fractions, this monograph presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. 1948 edition.
Continued Fractions
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Author : Lisa Lorentzen
language : en
Publisher: atlantis press
Release Date : 2008
Continued Fractions written by Lisa Lorentzen and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Continued Fractions consists of two volumes -- Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given.This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.
The Metrical Theory Of Jacobi Perron Algorithm
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Author : F. Schweiger
language : en
Publisher: Springer
Release Date : 2006-11-15
The Metrical Theory Of Jacobi Perron Algorithm written by F. Schweiger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Continued Fractions With Applications
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Author : L. Lorentzen
language : en
Publisher: North Holland
Release Date : 1992-11-08
Continued Fractions With Applications written by L. Lorentzen and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-08 with Computers categories.
This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.
Continued Fractions
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Author : Doug Hensley
language : en
Publisher: World Scientific
Release Date : 2006-03-01
Continued Fractions written by Doug Hensley and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-01 with Mathematics categories.
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.