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Invariant and attracting sets of Volterra difference equations with delays. (English) Zbl 1065.39021

The asymptotic properties, stability, existence of invariant sets and estimation of the basin of attraction are important in the theories of differential, difference and delayed differential equations. In this paper the author develops techniques for determinig the invariant and attracting sets of Volterra difference equations with delay. In case of an equilibrium solution, the basin of attraction becomes the domain of attraction of the asymptotic stability of the system. Two examples are given.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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