| 书目名称 | Elementary Symplectic Topology and Mechanics | | 编辑 | Franco Cardin | | 视频video | | | 丛书名称 | Lecture Notes of the Unione Matematica Italiana | | 图书封面 |  | | 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-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 oscillatin | | 出版日期 | Book 2015 | | 关键词 | 53D05,53D12,37J05,37J10,35F2,58E05,53Z05; Hamilton-Jacobi equations; Lusternik-Schnirelman theory; Mors | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-11026-4 | | isbn_softcover | 978-3-319-11025-7 | | isbn_ebook | 978-3-319-11026-4Series ISSN 1862-9113 Series E-ISSN 1862-9121 | | issn_series | 1862-9113 | | copyright | Springer International Publishing Switzerland 2015 |
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发表于 2025-3-21 16:59:55
