Geometric theory of discrete nonautonomous dynamical systems / by Christian Potzsche
- 作者： Potzsche, Christian.
- 其他作者：
- 其他題名：
- Springer eBooks
- 出版： Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg 2010
- 叢書名： Lecture notes in mathematics ,2002
- 主題： Differentiable dynamical systems. , Differential equations, Linear. , Mathematics. , Dynamical Systems and Ergodic Theory.
- ISBN： 9783642142581 (electronic bk.) 、 9783642142574 (paper)
- URL：
電子書
-
讀者標籤：
- 系統號： 005176236 | 機讀編目格式
館藏資訊
Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.