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Nonautonomous dynamical systems / Peter E. Kloeden, Martin Rasmussen.
- Format:
- Book
- Author/Creator:
- Kloeden, Peter E., author.
- Rasmussen, Martin, 1975- author.
- Series:
- Mathematical surveys and monographs ; Volume 176.
- Mathematical surveys and monographs ; Volume 176
- Language:
- English
- Subjects (All):
- Dynamics.
- Ergodic theory.
- Stability.
- Physical Description:
- 1 online resource (viii, 264 pages) : illustrations.
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2011]
- Language Note:
- English
- Summary:
- 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.
- Contents:
- Cover
- Title page
- Contents
- Preface
- Autonomous dynamical systems
- Nonautonomous dynamical systems
- Attractors
- Morse decompositions
- Linear systems
- Invariant manifolds
- Lyapunov functions
- Bifurcations
- Set-valued nonautonomous dynamical systems
- Nonautonomous semi-dynamical systems
- Approximation and perturbation of attractors
- Infinite-dimensional systems
- Switching and control systems
- Random dynamical systems
- Synchronization
- Appendix
- Bibliography
- Index
- Back Cover.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references (pages 253-262) and index.
- Description based on print version record.
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 1-4704-1403-1
- OCLC:
- 898200164
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