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Titlebook: Elementary Symplectic Topology and Mechanics; Franco Cardin Book 2015 Springer International Publishing Switzerland 2015 53D05,53D12,37J05

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發(fā)表于 2025-3-21 16:59:55 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Elementary Symplectic Topology and Mechanics
編輯Franco Cardin
視頻videohttp://file.papertrans.cn/308/307428/307428.mp4
叢書名稱Lecture Notes of the Unione Matematica Italiana
圖書封面Titlebook: Elementary Symplectic Topology and Mechanics;  Franco Cardin Book 2015 Springer International Publishing Switzerland 2015 53D05,53D12,37J05
描述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-H?rmander 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 oscillatin
出版日期Book 2015
關(guān)鍵詞53D05,53D12,37J05,37J10,35F2,58E05,53Z05; Hamilton-Jacobi equations; Lusternik-Schnirelman theory; Mors
版次1
doihttps://doi.org/10.1007/978-3-319-11026-4
isbn_softcover978-3-319-11025-7
isbn_ebook978-3-319-11026-4Series ISSN 1862-9113 Series E-ISSN 1862-9121
issn_series 1862-9113
copyrightSpringer International Publishing Switzerland 2015
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沙發(fā)
發(fā)表于 2025-3-21 23:07:54 | 只看該作者
The Emergence of Living Lab Methodsarbitrary Lagrangian function ., convex in the velocities .. The result can be obtained in the geometric setup of symplectic geometry using the Hamiltonian description of the problem: the joint use of the theory of Poincaré-Cartan Integral Invariant and Young Inequality rapidly leads to the thesis.
板凳
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Future of World Commercial Fisheries on Schr?dinger equation and on its asymptotic solutions. The purpose is that of indicating, rapidly indeed, the profound connections among symplectic geometry, geometric solutions to H-J equations and solutions to Schr?dinger equation in the so-called semi-classical limit: . (. is the Planck consta
地板
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Lecture Notes of the Unione Matematica Italianahttp://image.papertrans.cn/e/image/307428.jpg
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https://doi.org/10.1007/978-0-387-68316-4ints of functions. We will move in many directions, but mainly using constructions that are taken from the techniques in symplectic geometry described up to now. In particular, those on generating functions for Lagrangian submanifolds.
8#
發(fā)表于 2025-3-22 23:20:37 | 只看該作者
A Short Introduction to the Asymptotic Theory of Rapidly Oscillating Integrals, on Schr?dinger equation and on its asymptotic solutions. The purpose is that of indicating, rapidly indeed, the profound connections among symplectic geometry, geometric solutions to H-J equations and solutions to Schr?dinger equation in the so-called semi-classical limit: . (. is the Planck constant).
9#
發(fā)表于 2025-3-23 02:04:13 | 只看該作者
Notes on Lusternik-Schnirelman and Morse Theories,ints of functions. We will move in many directions, but mainly using constructions that are taken from the techniques in symplectic geometry described up to now. In particular, those on generating functions for Lagrangian submanifolds.
10#
發(fā)表于 2025-3-23 08:22:06 | 只看該作者
Long-Term Outcomes for Living Donors,We say that a smooth manifold . is a . if it is given together with a 2-form .?∈?..(.) which is . we denote with . the evaluation of a .-form . on . vectors ..,?.,?...
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