| 书目名称 | Index Theory for Symplectic Paths with Applications | | 编辑 | Yiming Long | | 视频video | | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | This book is based upon my monograph Index Theory for Hamiltonian Systems with Applications published in 1993 in Chinese, and my notes for lectures and courses given at Nankai University, Brigham Young University, ICTP-Trieste, and the Institute of Mathematics of Academia Sinica during the last ten years. The aim of this book is twofold: (1) to give an introduction to the index theory for symplectic matrix paths and its iteration theory, which form a basis for the Morse theoretical study on Hamilto nian systems, and to give applications of this theory to periodic boundary value problems of nonlinear Hamiltonian systems. Here the iteration theory means the index theory of iterations of periodic solutions and symplectic matrix paths. (2) to serve as a reference book on these topics. There are many different ways to introduce the index theory for symplectic paths in order to establish Morse type index theory of Hamiltonian systems. In this book, I have chosen a relatively elementary way, i.e., the homotopy classification method of symplectic matrix paths. It depends only on linear algebra, point set topology, and certain basic parts of linear functional analysis. I have tried to make | | 出版日期 | Book 2002 | | 关键词 | Boundary value problem; functional analysis; index theory; perturbation; perturbation theory; symplectic | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-8175-3 | | isbn_softcover | 978-3-0348-9466-1 | | isbn_ebook | 978-3-0348-8175-3Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Basel AG 2002 |
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发表于 2025-3-21 19:55:57
