Discrete Lagrangian Reduction Discrete Euler Poincar Equations And Semidirect Products
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Discrete Lagrangian Reduction Discrete Euler Poincar Equations And Semidirect Products
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Author : Alexander I. Bobenko
language : en
Publisher:
Release Date : 1999
Discrete Lagrangian Reduction Discrete Euler Poincar Equations And Semidirect Products written by Alexander I. Bobenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Discrete Lagrangian Reduction Discret Euler Poincar Equations And Semidirect Products
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Author : Aleksandr I. Bobenko
language : en
Publisher:
Release Date : 1999
Discrete Lagrangian Reduction Discret Euler Poincar Equations And Semidirect Products written by Aleksandr I. Bobenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Lagrangian Reduction By Stages
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Author : Hernán Cendra
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Lagrangian Reduction By Stages written by Hernán Cendra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler-Poincare reduction (for the case in which the configuration space is a Lie group) as well as Euler-Poincare reduction for semidirect products.
The Problem Of Integrable Discretization
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Author : Yuri B. Suris
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Problem Of Integrable Discretization written by Yuri B. Suris and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.
Lagrangian Reduction By Stages
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Author : Hernn Cendra
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-06-15
Lagrangian Reduction By Stages written by Hernn Cendra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-15 with Mathematics categories.
This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages}. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler-Poincare reduction (for the case in which the configuration space is a Lie group) as well as Euler-Poincare reduction for semidirect products. The context established for this theory is a Lagrangian analogue of the bundle picture on the Hamiltonian side. In this picture, we develop a category that includes, as a special case, the realization of the quotient of a tangent bundle as the Whitney sum of the tangent of the quotient bundle with the associated adjoint bundle. The elements of this new category, called the Lagrange-Poincare category, have enough geometric structure so that the category is stable under the procedure of Lagrangian reduction. Thus, reduction may be repeated, giving the desired context for reduction by stages. Our category may be viewed as a Lagrangian analog of the category of Poisson manifolds in Hamiltonian theory. We also give an intrinsic and geometric way of writing the reduced equations, called the Lagrange-Poincare equations, using covariant derivatives and connections. In addition, the context includes the interpretation of cocycles as curvatures of connections and is general enough to encompass interesting situations involving both semidirect products and central extensions. Examples are given to illustrate the general theory. In classical Routh reduction one usually sets the conserved quantities conjugate to the cyclic variables equal to a constant. In our development, we do not require the imposition of this constraint. For the general theory along these lines, we refer to the complementary work of [2000], which studies the Lagrange-Routh equations.
Quantization Of Singular Symplectic Quotients
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Author : N.P. Landsman
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Quantization Of Singular Symplectic Quotients written by N.P. Landsman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.
Acta Numerica 2001 Volume 10
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 2001-08-23
Acta Numerica 2001 Volume 10 written by Arieh Iserles 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 2001-08-23 with Mathematics categories.
An annual volume presenting substantive survey articles in numerical analysis and scientific computing.
The Geometry Of Infinite Dimensional Groups
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Author : Boris Khesin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-28
The Geometry Of Infinite Dimensional Groups written by Boris Khesin 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 2008-09-28 with Mathematics categories.
This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
Mathematics Unlimited 2001 And Beyond
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Author : Björn Engquist
language : en
Publisher: Springer
Release Date : 2017-04-05
Mathematics Unlimited 2001 And Beyond written by Björn Engquist and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Mathematics categories.
This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.
Geometry Mechanics And Dynamics
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Author : Dong Eui Chang
language : en
Publisher: Springer
Release Date : 2015-04-16
Geometry Mechanics And Dynamics written by Dong Eui Chang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Mathematics categories.
This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.