Non-autonomous dynamical systems (Q256789)
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scientific article; zbMATH DE number 6553078
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-autonomous dynamical systems |
scientific article; zbMATH DE number 6553078 |
Statements
Non-autonomous dynamical systems (English)
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10 March 2016
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skew-product semiflow
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Morse decomposition
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Morse-Smale system
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cocycle attractor
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pullback attractor
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uniform attractor
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This review paper consists of six sections.NEWLINENEWLINEIn Section 1 the authors present some notions and facts for autonomous dynamical systems: compact global attractors, gradient-like dynamical systems, Morse decomposition of attractors, Morse-Smale dynamical systems, parameter dependence of global attractors.NEWLINENEWLINESection 2 is dedicated to nonautonomous dynamical systems: two-parameter semigroups, cocycles, skew-product dynamical systems and their attractors. The relation between different types of attractors, such as forward attractors, uniform attractors, cocycle attractors and pull-back attractors, are studied.NEWLINENEWLINEIn the third section the problem of Morse decomposition of global attractors for skew-product dynamical systems is studied.NEWLINENEWLINEThe fourth section is dedicated to the study of global attractors for nonautonomous perturbations of gradient-like autonomous dynamical systems. The authors give a description of the structure of global attractors for this class of nonautonomous dynamical systems.NEWLINENEWLINEIn the last two sections the Morse theory of global attractors and Morse-Smale nonautonomous dynamical systems are studied.
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