| 书目名称 | Normally Hyperbolic Invariant Manifolds |
| 副标题 | The Noncompact Case |
| 编辑 | Jaap Eldering |
| 视频video | |
| 概述 | A gentle introduction: examples, history, overview of methods.Bridges nonlinear dynamics and differential geometry.Includes various new results in bounded geometry.Completely worked out persistence pr |
| 丛书名称 | Atlantis Studies in Dynamical Systems |
| 图书封面 |  |
| 描述 | .This monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems..First, normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due to noncompactness are discussed in great detail with examples..The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-known results by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompactness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed to analyze ODEs in a differential geometric context..Finally, the main result is extended to time and parameter dependent systems and overflowing invariant manifolds.. |
| 出版日期 | Book 2013 |
| 关键词 | Bounded geometry; Dynamical systems; Noncompactness; Normally hyperbolic invariant manifolds; Persistenc |
| 版次 | 1 |
| doi | https://doi.org/10.2991/978-94-6239-003-4 |
| isbn_softcover | 978-94-6239-042-3 |
| isbn_ebook | 978-94-6239-003-4Series ISSN 2213-3526 Series E-ISSN 2213-3534 |
| issn_series | 2213-3526 |
| copyright | Atlantis Press and the author 2013 |
发表于 2025-3-21 16:44:19
