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Uniform convergence and transitivity

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  • Román-Flores, Heriberto

Abstract

Let (X,d) be a metric space and fn:X→X a sequence of continuous functions such that (fn) converges uniformly to a function f. If fn is transitive for all n∈N, then the purpose of this work is, on the one hand, to show that f is not necessarily transitive and, on the other, to give sufficient conditions for the transitivity of the limit function f.

Suggested Citation

  • Román-Flores, Heriberto, 2008. "Uniform convergence and transitivity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 148-153.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:148-153
    DOI: 10.1016/j.chaos.2006.10.052
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    References listed on IDEAS

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    1. Román-Flores, Heriberto & Chalco-Cano, Y., 2005. "Robinson’s chaos in set-valued discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 33-42.
    2. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
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    Cited by:

    1. Yan, Kesong & Zeng, Fanping & Zhang, Gengrong, 2011. "Devaney’s chaos on uniform limit maps," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 522-525.

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