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    游杰. 一类广义帐篷映射的Devaney混沌性[J]. 内江师范学院学报, 2018, (4): 53-56. DOI:10.13603/j.cnki.51-1621/z.2018.04.010
    引用本文: 游杰. 一类广义帐篷映射的Devaney混沌性[J]. 内江师范学院学报, 2018, (4): 53-56.DOI:10.13603/j.cnki.51-1621/z.2018.04.010
    shu
    YOU Jie. Chaos of A Class of Generalized Tent Mapping[J]. Journal of Neijiang Normal University, 2018, (4): 53-56. DOI:10.13603/j.cnki.51-1621/z.2018.04.010
    Citation: YOU Jie. Chaos of A Class of Generalized Tent Mapping[J].Journal of Neijiang Normal University, 2018, (4): 53-56.DOI:10.13603/j.cnki.51-1621/z.2018.04.010
    shu

    一类广义帐篷映射的Devaney混沌性

    Chaos of A Class of Generalized Tent Mapping

      摘要
    • 摘要:研究了0, 1上一类推广的帐篷映射φ的Devaney混沌性.证明了一定参数条件下, 对任意0, 1的子区间J, 存在正整数n, 使得φn (J) =0, 1, 从而推出在该参数条件下φ是拓扑传递的.由于区间上连续自映射的拓扑传递性等价于Devaney混沌性, 因而可推知φ在该参数条件下是Devaney混沌的.

      Abstract:The chaos of a class of generalized tent mappingsφon 0, 1is studied.It is proved that under particular parameter conditions, for any sub-interval Jof0, 1, there exists a positive integer which enablesφn (J) , thus it can be derived that the mappingsφunder these conditions are topologically transitive.Since topological transitivity of a continuous selfmapping on an interval is equivalent to Devaney chaos, then it can be inferred thatφunder these conditions is Devaney chaos.

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