Nonautonomous Morse Decompositions

Part of the Lecture Notes in Mathematics book series (LNM, volume 1907)

The global asymptotic behavior of dynamical systems on compact metric spaces can be described via Morse decompositions. Their components, the so-called Morse sets, are obtained as intersections of attractors and repellers. In this chapter, nonautonomous generalizations of the Morse decomposition are established with respect to the notions of past and future attractivity and repulsivity. The dynamical properties of these decompositions are discussed, and nonautonomous Lyapunov functions which are constant on the Morse sets are constructed explicitly. Furthermore, Morse decompositions of one-dimensional and linear systems are analyzed.


Linear System Lyapunov Function Linear Subspace Limit Relation Random Dynamical System 
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© Springer-Verlag Berlin Heidelberg 2007

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