Generalized Notions Of Continued Fractions
DOWNLOAD
Download Generalized Notions Of Continued Fractions PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Generalized Notions Of Continued Fractions book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Generalized Notions Of Continued Fractions
DOWNLOAD
Author : Juan Fernández Sánchez
language : en
Publisher: CRC Press
Release Date : 2023-07-20
Generalized Notions Of Continued Fractions written by Juan Fernández Sánchez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-20 with Mathematics categories.
Ancient times witnessed the origins of the theory of continued fractions. Throughout time, mathematical geniuses such as Euclid, Aryabhata, Fibonacci, Bombelli, Wallis, Huygens, or Euler have made significant contributions to the development of this famous theory, and it continues to evolve today, especially as a means of linking different areas of mathematics. This book, whose primary audience is graduate students and senior researchers, is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions, including generalized Lehner, simple, and Hirzebruch-Jung continued fractions. After deriving invariant ergodic measures for each of the underlying transformations on [0,1] it is shown that any of the famous formulas, going back to Khintchine and Levy, carry over to more general settings. Complementing these results, the entropy of the transformations is calculated and the natural extensions of the dynamical systems to [0,1]2 are analyzed. Features Suitable for graduate students and senior researchers Written by international senior experts in number theory Contains the basic background, including some elementary results, that the reader may need to know before hand, making it a self-contained volume
Continued Fractions
DOWNLOAD
Author : Andrew M Rockett
language : en
Publisher: World Scientific Publishing Company
Release Date : 1992-08-08
Continued Fractions written by Andrew M Rockett and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-08 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. Request Inspection Copy
Continued Fractions
DOWNLOAD
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.
A Convergence Theorem For Noncommutative Continued Fractions
DOWNLOAD
Author : Wyman Fair
language : en
Publisher:
Release Date : 1970
A Convergence Theorem For Noncommutative Continued Fractions written by Wyman Fair and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Continued fractions categories.
Continued Fractions
DOWNLOAD
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.
Continued Fractions
DOWNLOAD
Author : Aleksandr I?Akovlevich Khinchin
language : en
Publisher: Courier Corporation
Release Date : 1997-05-14
Continued Fractions written by Aleksandr I?Akovlevich Khinchin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-14 with Mathematics categories.
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.
Analytic Theory Of Continued Fractions
DOWNLOAD
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
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 1961
Continued Fractions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.
Continued Fractions With Applications
DOWNLOAD
Author : L. Lorentzen
language : en
Publisher: North-Holland
Release Date : 1992-05
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 1992-05 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.
Convergence Of Some Generalized Continued Fractions
DOWNLOAD
Author : Marcelis Gerrit Bruin
language : en
Publisher:
Release Date : 1979
Convergence Of Some Generalized Continued Fractions written by Marcelis Gerrit Bruin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.