**Mathematical Surveys and Monographs**

Volume: 176;
2011;
264 pp;
Hardcover

MSC: Primary 37;

Print ISBN: 978-0-8218-6871-3

Product Code: SURV/176

List Price: $89.00

Individual Member Price: $71.20

**Electronic ISBN: 978-1-4704-1403-0
Product Code: SURV/176.E**

List Price: $89.00

Individual Member Price: $71.20

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#### Supplemental Materials

# Nonautonomous Dynamical Systems

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*Peter E. Kloeden; Martin Rasmussen*

The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched.

With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.

#### Table of Contents

# Table of Contents

## Nonautonomous Dynamical Systems

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Autonomous dynamical systems 110 free
- Nonautonomous dynamical systems 2332
- Attractors 3746
- Morse decompositions 6978
- Linear systems 7988
- Invariant manifolds 105114
- Lyapunov functions 129138
- Bifurcations 147156
- Set-valued nonautonomous dynamical systems 169178
- Nonautonomous semi-dynamical systems 185194
- Approximation and perturbation of attractors 191200
- Infinite-dimensional systems 205214
- Switching and control systems 213222
- Random dynamical systems 227236
- Synchronization 235244
- Appendix 251260
- Bibliography 253262
- Index 263272 free
- Back Cover Back Cover1274

#### Readership

Graduate students and research mathematicians interested in dynamical systems.