Titlebook: Attractivity and Bifurcation for Nonautonomous Dynamical Systems; Martin Rasmussen Book 2007 Springer-Verlag Berlin Heidelberg 2007 Nonaut

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Notions of Attractivity and Bifurcation,for nonautonomous dynamical systems. By a bifurcation and transition, a qualitative change of attractivity or repulsivity is meant. Due to the nonautonomous framework, it is distinguished between four distinct points of view concerning di.erent time domains. The notions of attractivity and repulsivi

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Nonautonomous Morse Decompositions,s 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 Lyapun

Valves

LinearSystems,ues requires linear theory. This is due to the fact that in many cases, stability properties of solutions can be derived from the linearization along the solution, the so-called variational equation. In this chapter, methods are provided for the analysis of linear systems with respect to the notions

揭穿真相

Nonlinear Systems,r an equilibrium, a periodic solution or—in the nonautonomous context—an arbitrary solution. The construction of stable and unstable invariant manifolds goes back to . [136] and . [73]. In the sequel, the theory was extended from hyperbolic to nonhyperbolic systems, from finite to infinite dimension

拔出

Bifurcations in Dimension One,pitchfork bifurcation, both for nonautonomous bifurcations and transitions..In this chapter, only the continuous case of ordinary differential equations is treated. For analogous results in the context of difference equations, see . [145].

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