Abstract
This paper is concerned with time-varying discrete dynamical systems in Banach spaces. A criterion of chaos induced by coupled-expansion for time-varying systems is first established and then the persistence of coupled-expansion is considered for time-varying systems under small time-varying perturbations, under which the perturbed system is shown chaotic in the strong sense of Li–Yorke. By applying this result, a map with a regular and nondegenerate snap-back repeller is shown to be still chaotic in the strong sense of Li–Yorke under small time-varying perturbations.
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