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A note on uniform convergence and transitivity

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  • Li, Risong

Abstract

In this paper, let (X,d) be a metric space. Let fn: X→X be a sequence of continuous and topologically transitive functions such that (fn) converges uniformly to a function f. It is shown that if (X,d) is compact and perfect, limn→∞d∞fnn,fn=0 and fnn(x) is dense in X for some x∈X, then f is totally transitive. We also present a sufficient condition for f to be topologically transitive (resp. syndetically transitive). Furthermore, we give a sufficient condition for f to be topologically weak mixing (resp. topologically mixing).

Suggested Citation

  • Li, Risong, 2012. "A note on uniform convergence and transitivity," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 759-764.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:6:p:759-764
    DOI: 10.1016/j.chaos.2012.02.007
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