Описание: The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytopes, a convex polyhedron which sits inside the dual of the Lie algebra of G. This book is suitable for researchers and can be used as a semester text.
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytope, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. For instance, the first chapter is largely devoted to the Delzant theorem, which says that there is a one-one correspondence between certain types of moment polytopes and certain types of symplectic G-spaces. (One of the most challenging unsolved problems in symplectic geometry is to determine to what extent Delzant's theorem is true of every compact symplectic G-Space.)
The moment polytope also encodes quantum information about the actions of G. Using the methods of geometric quantization, one can frequently convert this action into a representations, p, of G on a Hilbert space, and in some sense the moment polytope is a diagrammatic picture of the irreducible representations of G which occur as subrepresentations of p. Precise versions of this item of folklore are discussed in Chapters 3 and 4. Also, midway through Chapter 2 a more complicated object is discussed: the Duistermaat-Heckman measure, and the author explains in Chapter 4 how one can read off from this measure the approximate multiplicities with which the irreducible representations of G occur in p. This gives an excuse to touch on some results which are in themselves of great current interest: the Duistermaat-Heckman theorem, the localization theorems in equivariant cohomology of Atiyah-Bott and Berline-Vergne and the recent extremely exciting generalizations of these results by Witten, Jeffrey-Kirwan, Lalkman, and others.
The last two chapters of this book are a self-contained and somewhat unorthodox treatment of the theory of toric varieties in which the usual hierarchal relation of complex to symplectic is reversed. This book is addressed to researchers
Автор: Sergej B. Kuksin Название: Nearly Integrable Infinite-Dimensional Hamiltonian Systems ISBN: 3540571612 ISBN-13(EAN): 9783540571612 Издательство: Springer Рейтинг: Цена: 3492.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph is devoted to partial differential equations (PDEs) of Hamiltonian form. For each equation, a KAM-like theorem is proved, and then applied to classical nonlinear PDEs with one-dimensional space variables, such as the nonlinear string and nonlinear Schroedinger equations.
Автор: Michael Ryan Название: Hamiltonian Cosmology ISBN: 3540057412 ISBN-13(EAN): 9783540057413 Издательство: Springer Рейтинг: Цена: 11753.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Piotr T. Chrusciel; Jacek Jezierski; Jerzy Kijowsk Название: Hamiltonian Field Theory in the Radiating Regime ISBN: 3642076815 ISBN-13(EAN): 9783642076817 Издательство: Springer Рейтинг: Цена: 11753.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Birgit Jacob; Hans J. Zwart Название: Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces ISBN: 3034808119 ISBN-13(EAN): 9783034808118 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems.
Автор: Xavier Leoncini; Marc Leonetti Название: From Hamiltonian Chaos to Complex Systems ISBN: 1461469619 ISBN-13(EAN): 9781461469612 Издательство: Springer Рейтинг: Цена: 22203.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book reviews progress in non-linear dynamics and statistical physics with an emphasis on complex systems, showing how tools developed for dynamical systems, nonlinear physics and statistical dynamics can open a panorama of research in physics and beyond.
Автор: Gerdjikov Vladimir Название: Integrable Hamiltonian Hierarchies ISBN: 3642095771 ISBN-13(EAN): 9783642095771 Издательство: Springer Рейтинг: Цена: 18284.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
Автор: Vivek S. Borkar; Vladimir Ejov; Jerzy A. Filar; Gi Название: Hamiltonian Cycle Problem and Markov Chains ISBN: 1489992278 ISBN-13(EAN): 9781489992277 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be carried out.
Автор: Joaqu?n Delgado; Ernesto A. Lacomba; Jaume Llibre; Название: New Advances in Celestial Mechanics and Hamiltonian Systems ISBN: 0306481170 ISBN-13(EAN): 9780306481178 Издательство: Springer Рейтинг: Цена: 25155.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Includes discussion topics such as: periodic orbits and choreographies in the n-body problem, singularities in few body problems, central configurations, restricted three body problem, geometrical mechanics, dynamics of charged problems, and area preserving maps and Arnold diffusion. This book is aimed at young researchers and graduated students.
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