Abstract
We consider abelian nonautonomous dynamical systems F=(fn) on compact spaces X which are moreover transitive; that is, the limit set of some point x∈X coincides with the whole space X, and we extend some results of [1]. More precisely, we show that such F must be either pointwise sensitive or uniformly rigid and almost equicontinuous. Moreover, we prove that if the set of equicontinuity points of F has nonempty interior, then it coincides with the set of transitive points and F will be equicontinuous if and only if it is minimal. Next, we assume that the sequence (fn) converges uniformly to a transitive map f, and we prove that if f is minimal or equicontinuous then F is either sensitive or equicontinuous, minimal and uniformly rigid. We also study chaos for F, and we prove that Devaney chaos implies Li-Yorke chaos.
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