| 书目名称 | Shadowing in Dynamical Systems |
| 副标题 | Theory and Applicati |
| 编辑 | Ken Palmer |
| 视频video | |
| 丛书名称 | Mathematics and Its Applications |
| 图书封面 |  |
| 描述 | In this book the theory of hyperbolic sets is developed, bothfor diffeomorphisms and flows, with an emphasis on shadowing. We showthat hyperbolic sets are expansive and have the shadowing property.Then we use shadowing to prove that hyperbolic sets are robust underperturbation, that they have an asymptotic phase property and alsothat the dynamics near a transversal homoclinic orbit is chaotic..It turns out that chaotic dynamical systems arising in practice arenot quite hyperbolic. However, they possess enough hyperbolicity toenable us to use shadowing ideas to give computer-assisted proofs thatcomputed orbits of such systems can be shadowed by true orbits forlong periods of time, that they possess periodic orbits of longperiods and that it is really true that they are chaotic. ..Audience:. This book is intended primarily for research workersin dynamical systems but could also be used in an advanced graduatecourse taken by students familiar with calculus in Banach spaces andwith the basic existence theory for ordinary differential equations. |
| 出版日期 | Book 2000 |
| 关键词 | Manifold; Morphism; calculus; computer; dynamical systems; dynamische Systeme; equation; ordinary different |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4757-3210-8 |
| isbn_softcover | 978-1-4419-4827-4 |
| isbn_ebook | 978-1-4757-3210-8 |
| copyright | Springer Science+Business Media Dordrecht 2000 |
发表于 2025-3-21 18:58:05
