Distributional chaos for triangular maps
Distributional chaos for triangular maps
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DOI：
10.1016/j.chaos.2003.12.105
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发表时间：
2004-09
影响因子：
7.8
通讯作者：
J. Smítal;M. Stefánková
中科院分区：
文献类型：
--
作者：
J. Smítal;M. Stefánková
本文证明了正方形的三角映射F具有以下性质：（i）F是2∞型的，但具有正的拓扑熵;我们记得Kolyada在1992年给出了类似的例子，但我们的论证要简单得多。(ii)F在广义上是分布混沌的，但在Schweizer和Smítal [Trans.Amer.Math.Soc.344（1994）737]所介绍的意义上不是分布混沌的。换句话说，存在由F生成的下分布函数Φ xy和上分布函数Φxy，使得Φxy 1和Φxy（0+）<1，并且没有分布函数Φuv和Φuv，使得当0<t<t时，Φuv 1和Φuv（t）=0。我们还表明，本文中使用的两个概念的分布混沌，连续映射的紧度量空间，是拓扑共轭的不变量。
In this paper we exhibit a triangular map F of the square with the following properties: (i) F is of type 2∞but has positive topological entropy; we recall that similar example was given by Kolyada in 1992, but our argument is much simpler. (ii) F is distributionally chaotic in the wider sense, but not distributionally chaotic in the sense introduced by Schweizer and Smítal [Trans. Amer. Math. Soc. 344 (1994) 737]. In other words, there are lower and upper distribution functions Φxyand Φxy∗generated by F such that Φxy∗≡1 and Φxy(0+)<1, and no distribution functions Φuv, and Φuv∗such that Φuv∗≡1 and Φuv(t)=0 whenever 0<t<ϵ, for some ϵ>0. We also show that the two notions of distributional chaos used in the paper, for continuous maps of a compact metric space, are invariants of topological conjugacy.