Cheban, D. N. On the structure of the Levinson center of a dissipative dynamical system with hyperbolicity condition on the closure of the set of recurrent motions. (Russian) Zbl 0701.58040 Differ. Uravn. 26, No. 5, 913-914 (1990). A nonautonomous dynamical system is defined to be a triple ((X,T,\(\pi\)),(Y,T,\(\sigma\)),h) where (X,T,\(\pi\)) and (Y,T,\(\sigma\)) are dynamical systems (X,Y complete metric spaces, T the group of reals or integers) and h: \(X\to Y\) is a homomorphism of the first system onto the other. Under certain assumption of a hyperbolic type it is proved that the Levinson center of a dissipative nonautonomous dynamical system admits the spectral decomposition, like an Axiom A flow. The paper heavily depends on the papers by the same author in Differ. Uravn. 20, No.11, 2016-2018 (1984; Zbl 0567.58017) and Differ. Equations 22, 200-209 (1986); translation from Differ. Uravn. 22, No.2, 267-278 (1986; Zbl 0611.34033). Reviewer: J.Ombach MSC: 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 37D99 Dynamical systems with hyperbolic behavior 34D20 Stability of solutions to ordinary differential equations Keywords:chain recurrence; hyperbolic structure; nonautonomous dynamical system Citations:Zbl 0567.58017; Zbl 0611.34033 PDFBibTeX XMLCite \textit{D. N. Cheban}, Differ. Uravn. 26, No. 5, 913--914 (1990; Zbl 0701.58040)