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New criteria for exponential stability of variational difference equations. (English) Zbl 1120.39009

Author’s abstract: The aim of this work is to obtain very general characterizations for uniform exponential stability of variational difference equations, using Banach sequence spaces. We prove that a system of variational difference equations is uniformly exponentially stable if and only if there is a Banach sequence space \(B\), with certain properties, such that the set of all vectors with the corresponding orbits contained uniformly in \(B\) is of the second category. We apply our result at the study of the uniform exponential stability of linear skew-product flows.

MSC:

39A11 Stability of difference equations (MSC2000)
37C75 Stability theory for smooth dynamical systems
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