Hamiltonian Lie Algebroids
Author | : Christian Blohmann |
Publisher | : American Mathematical Society |
Total Pages | : 112 |
Release | : 2024-04-17 |
Genre | : Mathematics |
ISBN | : 147046909X |
View the abstract.
Download Hamiltonian Lie Algebroids full books in PDF, epub, and Kindle. Read online free Hamiltonian Lie Algebroids ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Christian Blohmann |
Publisher | : American Mathematical Society |
Total Pages | : 112 |
Release | : 2024-04-17 |
Genre | : Mathematics |
ISBN | : 147046909X |
View the abstract.
Author | : Kirill C. H. Mackenzie |
Publisher | : Cambridge University Press |
Total Pages | : 540 |
Release | : 2005-06-09 |
Genre | : Mathematics |
ISBN | : 0521499283 |
This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry andgeneral connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. As such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.
Author | : A. T. Fomenko |
Publisher | : CRC Press |
Total Pages | : 316 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 9782881241703 |
Second volume in the series, translated from the Russian, sets out new regular methods for realizing Hamilton's canonical equations in Lie algebras and symmetric spaces. Begins by constructing the algebraic embeddings in Lie algebras of Hamiltonian systems, going on to present effective methods for constructing complete sets of functions in involution on orbits of coadjoint representations of Lie groups. Ends with the proof of the full integrability of a wide range of many- parameter families of Hamiltonian systems that allow algebraicization. Annotation copyrighted by Book News, Inc., Portland, OR
Author | : Mónica Aymerich Valls |
Publisher | : |
Total Pages | : |
Release | : 2011 |
Genre | : |
ISBN | : |
It is well-known that the Poisson reduction of a hamiltonian system on the cotangent bundle of a manifold produces a hamiltonian system on a linear Poisson manifold. On the other hand, linear Poisson structures on a vector bundle $Â*$ may be described in terms of the canonical symplectic section of ${\mathcal T}̂AÂ*$, the $A$-tangent bundle to $Â*$. In fact, ${\mathcal T}̂AÂ*$ is a canonical symplectic Lie algebroid over the linear Poisson manifold $Â*$. In this master thesis, we discuss Lagrangian Lie subalgebroids of ${\mathcal T}̂AÂ*$. The base space of a Lagrangian Lie subalgebroid $L$ turns out to be a coisotropic submanifold $C$ of $Â*$. Thus, first we describe the local nature of $C$ when it is an affine subbundle of $Â*$ and then we describe the local nature of $L$. We expect that these results may be applied, in a future work, in the geometric formulation of Hamilton-Jacobi theory for reduced hamiltonian systems.
Author | : Jan Kubarski |
Publisher | : |
Total Pages | : 284 |
Release | : 2001 |
Genre | : Geometry, Diferential |
ISBN | : |
Author | : Camille Laurent-Gengoux |
Publisher | : Springer Science & Business Media |
Total Pages | : 470 |
Release | : 2012-08-27 |
Genre | : Mathematics |
ISBN | : 3642310907 |
Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.
Author | : Ana Cannas da Silva |
Publisher | : American Mathematical Soc. |
Total Pages | : 202 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780821809525 |
The volume is based on a course, ``Geometric Models for Noncommutative Algebras'' taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.
Author | : Tudor Ratiu |
Publisher | : Springer |
Total Pages | : 552 |
Release | : 1991-08-16 |
Genre | : Mathematics |
ISBN | : |
The papers in this volume are an outgrowth of some of the lectures and informal discussions that took place during the workshop on the geometry of Hamiltonian systems, held at the MSRI in Berkeley in June of 1989. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, numerical simulations and dynamical systems in general. The articles are of differing lengths and scopes; some are research announcements while others are surveys of particularly active areas of interest where the results can only be found in scattered research articles and preprints. In- cluded in the book is A.T. Fomenko's survey of the classification of integrable systems.
Author | : Jean-Paul Dufour |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2006-01-17 |
Genre | : Mathematics |
ISBN | : 3764373350 |
The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.
Author | : Jerrold E. Marsden |
Publisher | : Springer |
Total Pages | : 527 |
Release | : 2007-06-05 |
Genre | : Mathematics |
ISBN | : 3540724702 |
This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.