Metrical Theory Of Continued Fractions
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Author |
: M. Iosifescu |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 397 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9789401599405 |
ISBN-13 |
: 9401599408 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Metrical Theory of Continued Fractions by : M. Iosifescu
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 |
ISBN-10 |
: 9401599416 |
ISBN-13 |
: 9789401599412 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Metrical Theory of Continued Fractions by : M. Iosifescu
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 |
ISBN-10 |
: 9810210523 |
ISBN-13 |
: 9789810210526 |
Rating |
: 4/5 (23 Downloads) |
Synopsis Continued Fractions by : A. M. Rockett
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 |
ISBN-10 |
: OCLC:4061512 |
ISBN-13 |
: |
Rating |
: 4/5 (12 Downloads) |
Synopsis The Metrical Theory of Continued Fractions to the Nearest Integer by : Andrew Mansfield Rockett
Author |
: Wieb Bosma |
Publisher |
: |
Total Pages |
: 15 |
Release |
: 1987 |
ISBN-10 |
: OCLC:64859644 |
ISBN-13 |
: |
Rating |
: 4/5 (44 Downloads) |
Synopsis Metrical Theory for Optimal Continued Fractions by : Wieb Bosma
Author |
: Andrew Mansfield Rockett |
Publisher |
: |
Total Pages |
: |
Release |
: 1992 |
ISBN-10 |
: 9814439789 |
ISBN-13 |
: 9789814439787 |
Rating |
: 4/5 (89 Downloads) |
Synopsis Continued Fractions by : Andrew Mansfield Rockett
Author |
: Marius Iosifescu |
Publisher |
: |
Total Pages |
: 143 |
Release |
: 2011 |
ISBN-10 |
: 9732720492 |
ISBN-13 |
: 9789732720493 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Metrical Theory of Some Continued Fraction Expansions by : Marius Iosifescu
Author |
: Aleksandr I?Akovlevich Khinchin |
Publisher |
: Courier Corporation |
Total Pages |
: 114 |
Release |
: 1997-05-14 |
ISBN-10 |
: 9780486696300 |
ISBN-13 |
: 0486696308 |
Rating |
: 4/5 (00 Downloads) |
Synopsis Continued Fractions by : Aleksandr I?Akovlevich Khinchin
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 |
: Andrew M Rockett |
Publisher |
: World Scientific Publishing Company |
Total Pages |
: 200 |
Release |
: 1992-08-08 |
ISBN-10 |
: 9789813103412 |
ISBN-13 |
: 9813103418 |
Rating |
: 4/5 (12 Downloads) |
Synopsis Continued Fractions by : Andrew M Rockett
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 |
: F. Schweiger |
Publisher |
: Springer |
Total Pages |
: 117 |
Release |
: 2006-11-15 |
ISBN-10 |
: 9783540470106 |
ISBN-13 |
: 3540470107 |
Rating |
: 4/5 (06 Downloads) |
Synopsis The Metrical Theory of Jacobi-Perron Algorithm by : F. Schweiger