Multidimensional Continued Fractions
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Multidimensional Continued Fractions
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Author : Fritz Schweiger
language : en
Publisher: Oxford University Press, USA
Release Date : 2000
Multidimensional Continued Fractions written by Fritz Schweiger and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The book gives an up to date overview of various aspects of multidimensional continued fractions, which are here defined through iteration of piecewise fractional linear maps. This includes the algorithms of Jacobi-Perron, Güting, Brun, and Selmer but it also includes continued fractions on simplices which are related to interval exchange maps or the Parry-Daniels map. New classes of subtractive algorithms are also included and the metric properties of these algorithms can be therefore investigated by methods of ergodic theory. The recent connection between multiplicative ergodic theory and Diophantine approximation presented, as well as several results on convergence and Perron's approach to periodicity, which has never appeared in book despite being published in 1907. Further chapters include the basic properties of continued fractions in the complex plane, connections with Hausdorff dimension and the Kuzmin theory for multidimensional maps.
Geometry Of Continued Fractions
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Author : Oleg Karpenkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-15
Geometry Of Continued Fractions written by Oleg Karpenkov 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 2013-08-15 with Mathematics categories.
Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Geometry Of Continued Fractions
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Author : Oleg N. Karpenkov
language : en
Publisher: Springer Nature
Release Date : 2022-05-28
Geometry Of Continued Fractions written by Oleg N. Karpenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-28 with Mathematics categories.
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Multi Dimensional Continued Fraction Algorithms
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Author : A. J. Brentjes
language : en
Publisher:
Release Date : 1981
Multi Dimensional Continued Fraction Algorithms written by A. J. Brentjes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Algorithms categories.
Continued Fractions
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Author : Doug Hensley
language : en
Publisher: World Scientific
Release Date : 2006
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 with Mathematics categories.
"This book is the first authoritative and up-to-date survey of the history of Iraq from earliest times to the present in any language. It presents a concise narrative of the rich and varied history of this land, drawing on political, social, economic, artistic, technological, and intellectual material. It also includes excerpts from works of ancient, medieval, and modern literature written in Iraq, some of which are translated for the first time into English. The final chapters provide an introduction tothe history of archaeology in Iraq, set in the wider context of the development of archaeology into a scientific discipline. A special section highlights selected objects from the Iraq Museum, with emphasis on their cultural significance and current status in the aftermath of the looting in April 2003. The last chapter offers a unique guide to the complex international and national legal regimes for the protection of cultural heritage. The American-led invasion and occupation of Iraq are a turning point in Iraq's modern history, with important cultural consequences for all periods of its past. For all who seek to understand more fully the current situation, this book includes discussion of cultural and legal issues of the war and occupation, placing recent events in their full context."--pub. desc.
Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions
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Author : Gregory R. Maloney
language : en
Publisher:
Release Date : 2009
Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions written by Gregory R. Maloney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Thirty years ago, Effros and Shen classified the simple dimension groups with rank two. Every such group is parametrized by an irrational number, and can be constructed as an inductive limit using that number's continued fraction expansion. There is a natural generalization of continued fractions to higher dimensions, and this invites the following question: What dimension groups correspond to multidimensional continued fractions? We describe this class of groups and show how some properties of a continued fraction are reflected in the structure of its dimension group. We also consider a related issue: an Effros-Shen group has been shown to arise in a natural way from the tail equivalence relation on a certain sequence space. We describe a more general class of sequence spaces to which this construction can be applied to obtain other dimension groups, including dimension groups corresponding to multidimensional continued fractions.
Handbook Of Continued Fractions For Special Functions
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Author : Annie A.M. Cuyt
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-12
Handbook Of Continued Fractions For Special Functions written by Annie A.M. Cuyt 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 2008-04-12 with Mathematics categories.
Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!
2019 20 Matrix Annals
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Author : Jan de Gier
language : en
Publisher: Springer Nature
Release Date : 2021-02-10
2019 20 Matrix Annals written by Jan de Gier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions
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Author : Gregory R. Maloney
language : en
Publisher:
Release Date : 2009
Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions written by Gregory R. Maloney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Thirty years ago, Effros and Shen classified the simple dimension groups with rank two. Every such group is parametrized by an irrational number, and can be constructed as an inductive limit using that number's continued fraction expansion.There is a natural generalization of continued fractions to higher dimensions, and this invites the following question: What dimension groups correspond to multidimensional continued fractions? We describe this class of groups and show how some properties of a continued fraction are reflected in the structure of its dimension group.We also consider a related issue: an Effros-Shen group has been shown to arise in a natural way from the tail equivalence relation on a certain sequence space. We describe a more general class of sequence spaces to which this construction can be applied to obtain other dimension groups, including dimension groups corresponding to multidimensional continued fractions.
Women In Numbers Europe Iv
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Author : Ramla Abdellatif
language : en
Publisher: Springer Nature
Release Date : 2024-08-07
Women In Numbers Europe Iv written by Ramla Abdellatif and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-07 with Mathematics categories.
This volume contains research and expository content based on a wide variety of topics within modern number theory and arithmetic geometry. Research in this volume arises from or is connected with the Women in Numbers Europe (WiNE) IV conference held in summer 2022 in Utrecht, The Netherlands. The contents of this volume are of interest to professional mathematicians, graduate students, and researchers working in number theory, arithmetic geometry, and related areas.