Attractivity and Bifurcation for Nonautonomous Dynamical Systems [electronic resource] / by Martin Rasmussen.
- Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
- Lecture Notes in Mathematics, 0075-8434 ; 1907
Lecture Notes in Mathematics, 0075-8434 ; 1907
1 online resource (XI, 217 pages)
- Differential Equations.
Differentiable dynamical systems.
- Local subjects:
- Ordinary Differential Equations. (search)
Dynamical Systems and Ergodic Theory. (search)
- System Details:
- text file PDF
- Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.
- Notions of Attractivity and Bifurcation
Nonautonomous Morse Decompositions
Bifurcations in Dimension One
Bifurcations of Asymptotically Autonomous Systems.
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- Publisher Number:
- 10.1007/978-3-540-71225-1 doi
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- Restricted for use by site license.
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