Discrete Integrable Geometry And Physics
DOWNLOAD
Download Discrete Integrable Geometry And Physics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Discrete Integrable Geometry And Physics 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
Discrete Integrable Geometry And Physics
DOWNLOAD
Author : Alexander I. Bobenko
language : en
Publisher: Clarendon Press
Release Date : 1999
Discrete Integrable Geometry And Physics written by Alexander I. Bobenko and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Recent interactions between the fields of geometry, classical and quantum dynamical systems, and visualization of geometric objects such as curves and surfaces have led to the observation that most concepts of surface theory and of the theory of integrable systems have natural discreteanalogues. These are characterized by the property that the corresponding difference equations are integrable, and has led in turn to some important applications in areas of condensed matter physics and quantum field theory, amongst others. The book combines the efforts of a distinguished team ofauthors from various fields in mathematics and physics in an effort to provide an overview of the subject. The mathematical concepts of discrete geometry and discrete integrable systems are firstly presented as fundamental and valuable theories in themselves. In the following part these concepts areput into the context of classical and quantum dynamics.
Discrete Differential Geometry
DOWNLOAD
Author : Alexander I. Bobenko
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-14
Discrete Differential Geometry written by Alexander I. Bobenko and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-14 with Mathematics categories.
An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.
Discrete Differential Geometry
DOWNLOAD
Author : Alexander I. Bobenko TU Berlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-27
Discrete Differential Geometry written by Alexander I. Bobenko TU Berlin 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 2008-03-27 with Mathematics categories.
This is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. The carefully edited collection of essays gives a lively, multi-facetted introduction to this emerging field.
Discrete Systems And Integrability
DOWNLOAD
Author : J. Hietarinta
language : en
Publisher: Cambridge University Press
Release Date : 2016-09
Discrete Systems And Integrability written by J. Hietarinta and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09 with Mathematics categories.
A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.
Advances In Discrete Differential Geometry
DOWNLOAD
Author : Alexander I. Bobenko
language : en
Publisher: Springer
Release Date : 2016-08-12
Advances In Discrete Differential Geometry written by Alexander I. Bobenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-12 with Mathematics categories.
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.
Discrete Integrable Systems
DOWNLOAD
Author : J.J. Duistermaat
language : en
Publisher: Springer
Release Date : 2010-09-16
Discrete Integrable Systems written by J.J. Duistermaat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-16 with Mathematics categories.
This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, considered as automorphisms of rational elliptic surfaces. The theory of QRT maps arose from problems in mathematical physics, involving difference equations. The application of QRT maps to these and other problems in the literature, including Poncelet mapping and the elliptic billiard, is examined in detail. The link between elliptic fibrations and completely integrable Hamiltonian systems is also discussed. The book begins with a comprehensive overview of the subject, including QRT maps, singularity confinement, automorphisms of rational elliptic surfaces, action on homology classes, and periodic QRT maps. Later chapters cover these topics and more in detail. While QRT maps will be familiar to specialists in algebraic geometry, the present volume makes the subject accessible to mathematicians and graduate students in a classroom setting or for self-study.
Discrete Integrable Systems
DOWNLOAD
Author : J.J. Duistermaat
language : en
Publisher: Springer
Release Date : 2010-09-15
Discrete Integrable Systems written by J.J. Duistermaat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-15 with Mathematics categories.
This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, considered as automorphisms of rational elliptic surfaces. The theory of QRT maps arose from problems in mathematical physics, involving difference equations. The application of QRT maps to these and other problems in the literature, including Poncelet mapping and the elliptic billiard, is examined in detail. The link between elliptic fibrations and completely integrable Hamiltonian systems is also discussed. The book begins with a comprehensive overview of the subject, including QRT maps, singularity confinement, automorphisms of rational elliptic surfaces, action on homology classes, and periodic QRT maps. Later chapters cover these topics and more in detail. While QRT maps will be familiar to specialists in algebraic geometry, the present volume makes the subject accessible to mathematicians and graduate students in a classroom setting or for self-study.
Discrete Integrable Systems
DOWNLOAD
Author : Basil Grammaticos
language : en
Publisher: Springer
Release Date : 2004-06-22
Discrete Integrable Systems written by Basil Grammaticos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-22 with Science categories.
This volume consists of a set of ten lectures conceived as both introduction and up-to-date survey on discrete integrable systems. It constitutes a companion book to "Integrability of Nonlinear Systems" (Springer-Verlag, 2004, LNP 638, ISBN 3-540-20630-2). Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
Discrete Finite And Lie Groups
DOWNLOAD
Author : Pietro Giuseppe Fré
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-08-07
Discrete Finite And Lie Groups written by Pietro Giuseppe Fré and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-07 with Science categories.
In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects, treating its conceptual foundations in a proper logical order. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed.
Discrete Integrable Systems
DOWNLOAD
Author : Basil Grammaticos
language : en
Publisher:
Release Date : 2014-01-15
Discrete Integrable Systems written by Basil Grammaticos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.