Symplectic Techniques In Physics, Victor Guillemin, Shlomo Sternberg

Автор: Izu Vaisman
Название: Symplectic Geometry and Secondary Characteristic Classes
ISBN: 1475719620 ISBN-13(EAN): 9781475719628
Издательство: Springer
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Описание: Tondeur (43], and it indicates that the Maslov class is a secondary characteristic class of a complex trivial vector bundle endowed with a real reduction of its structure group. Arnold about the Maslov class (2], it is also pointed out without details that the Maslov class is characteristic in the category of vector bundles mentioned pre- viously.

Автор: Doslэ Ondřej, Elyseeva Julia, Simon Hilscher Roman
Название: Symplectic Difference Systems: Oscillation and Spectral Theory
ISBN: 3030193756 ISBN-13(EAN): 9783030193751
Издательство: Springer
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Цена: 11878.00 р.
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Описание: This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory.

Автор: Ond?ej Do?l?; Julia Elyseeva; Roman ?imon Hilscher
Название: Symplectic Difference Systems: Oscillation and Spectral Theory
ISBN: 3030193721 ISBN-13(EAN): 9783030193720
Издательство: Springer
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Цена: 16769.00 р.
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Описание: This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.

Автор: Jialin Hong; Xu Wang
Название: Invariant Measures for Stochastic Nonlinear Schr?dinger Equations
ISBN: 9813290684 ISBN-13(EAN): 9789813290686
Издательство: Springer
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Описание: This book provides some recent advance in the study of stochastic nonlinear Schr?dinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schr?dinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schr?dinger equations.