Elementary symplectic topology and mechanics

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the...

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Tác giả chính:	Cardin, Franco
Định dạng:	Sách
Ngôn ngữ:	English
Được phát hành:	Springer 2015
Những chủ đề:	Symplectic Contact topology Topology
Truy cập trực tuyến:	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57668
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spelling	oai:scholar.dlu.edu.vn:DLU123456789-576682023-11-11T05:49:15Z Elementary symplectic topology and mechanics Cardin, Franco Symplectic Contact topology Topology This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects. 2015-08-20T03:16:21Z 2015-08-20T03:16:21Z 2015 Book https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57668 en application/pdf Springer
institution	Thư viện Trường Đại học Đà Lạt
collection	Thư viện số
language	English
topic	Symplectic Contact topology Topology
spellingShingle	Symplectic Contact topology Topology Cardin, Franco Elementary symplectic topology and mechanics
description	This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.
format	Book
author	Cardin, Franco
author_facet	Cardin, Franco
author_sort	Cardin, Franco
title	Elementary symplectic topology and mechanics
title_short	Elementary symplectic topology and mechanics
title_full	Elementary symplectic topology and mechanics
title_fullStr	Elementary symplectic topology and mechanics
title_full_unstemmed	Elementary symplectic topology and mechanics
title_sort	elementary symplectic topology and mechanics
publisher	Springer
publishDate	2015
url	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57668
_version_	1782538185862021120

Elementary symplectic topology and mechanics

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