کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1891793 | 1043923 | 2012 | 6 صفحه PDF | دانلود رایگان |

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).In addition, for a compact metric space (X, d), suppose that the fn: X → X are continuous and converge uniformly to f. If for a given ε > 0, there exists a positive integer n0 such that for all n > n0 and all l > 0, d(fnl(x),fl(x))<ε for all x ∈ X, then the following statements hold:(1)f is syndetically sensitive (resp. cofinitely sensitive) whenever the fn are syndetically sensitive (resp. cofinitely sensitive).(2)f is multi-sensitive whenever the fn are multi-sensitive.(3)If f is sensitive (resp. cofinitely sensitive) with δ as a constant of sensitivity, then there exists an integer N > 0 such that fn is sensitive (resp. cofinitely sensitive) with 13δ as a constant of sensitivity for any n ⩾ N.(4)If f is multi-sensitive (resp. syndetically sensitive) with δ as a constant of sensitivity, then there exists an integer N > 0 such that fn is multi-sensitive (resp. syndetically sensitive) with 19δ as a constant of sensitivity for any n ⩾ N.
Journal: Chaos, Solitons & Fractals - Volume 45, Issue 6, June 2012, Pages 759–764