Index Theory for Symplectic Paths with Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2002
|
| Schriftenreihe: | Progress in Mathematics
207 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 this part of the book self-contained and at the same time include all of the major results on these topics so that researchers and students interested in them can read it without substantial difficulties, and can learn the main results in this area for their possible applications |
| Beschreibung: | 1 Online-Ressource (XXIV, 380 p) |
| ISBN: | 9783034881753 9783034894661 |
| DOI: | 10.1007/978-3-0348-8175-3 |
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Datensatz im Suchindex
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| discipline | Mathematik |
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| isbn | 9783034881753 9783034894661 |
| language | English |
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| spelling | Long, Yiming Verfasser aut Index Theory for Symplectic Paths with Applications by Yiming Long Basel Birkhäuser Basel 2002 1 Online-Ressource (XXIV, 380 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 207 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 this part of the book self-contained and at the same time include all of the major results on these topics so that researchers and students interested in them can read it without substantial difficulties, and can learn the main results in this area for their possible applications Mathematics Global differential geometry Differential Geometry Mathematik Periodische Lösung (DE-588)4199269-6 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Symplektische Gruppe (DE-588)4276585-7 gnd rswk-swf Indextheorie (DE-588)4161489-6 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Periodische Lösung (DE-588)4199269-6 s Symplektische Gruppe (DE-588)4276585-7 s Indextheorie (DE-588)4161489-6 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-8175-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Long, Yiming Index Theory for Symplectic Paths with Applications Mathematics Global differential geometry Differential Geometry Mathematik Periodische Lösung (DE-588)4199269-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd Symplektische Gruppe (DE-588)4276585-7 gnd Indextheorie (DE-588)4161489-6 gnd |
| subject_GND | (DE-588)4199269-6 (DE-588)4139943-2 (DE-588)4276585-7 (DE-588)4161489-6 |
| title | Index Theory for Symplectic Paths with Applications |
| title_auth | Index Theory for Symplectic Paths with Applications |
| title_exact_search | Index Theory for Symplectic Paths with Applications |
| title_full | Index Theory for Symplectic Paths with Applications by Yiming Long |
| title_fullStr | Index Theory for Symplectic Paths with Applications by Yiming Long |
| title_full_unstemmed | Index Theory for Symplectic Paths with Applications by Yiming Long |
| title_short | Index Theory for Symplectic Paths with Applications |
| title_sort | index theory for symplectic paths with applications |
| topic | Mathematics Global differential geometry Differential Geometry Mathematik Periodische Lösung (DE-588)4199269-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd Symplektische Gruppe (DE-588)4276585-7 gnd Indextheorie (DE-588)4161489-6 gnd |
| topic_facet | Mathematics Global differential geometry Differential Geometry Mathematik Periodische Lösung Hamiltonsches System Symplektische Gruppe Indextheorie |
| url | https://doi.org/10.1007/978-3-0348-8175-3 |
| work_keys_str_mv | AT longyiming indextheoryforsymplecticpathswithapplications |