P-chaos implies distributional chaos and chaos in the sense of Devaney with positive topological entropy
P-chaos implies distributional chaos and chaos in the sense of Devaney with positive topological entropy
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DOI：
10.1016/j.topol.2005.11.016
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发表时间：
2007-04
影响因子：
0.6
通讯作者：
T. Arai;Naotsugu Chinen
中科院分区：
文献类型：
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作者：
T. Arai;Naotsugu Chinen
设f是从紧度量空间X到自身的连续映射.称映射f是P-混沌的，如果它具有伪轨跟踪性质，且f的所有周期点的闭包等于X。我们证明了从连续统到自身的P-混沌映射在Devaney意义下是混沌的，并且具有正拓扑熵的1型分布混沌。
Let f be a continuous map from a compact metric space X to itself. The map f is called to be P-chaotic if it has the pseudo-orbit-tracing property and the closure of the set of all periodic points for f is equal to X. We show that every P-chaotic map from a continuum to itself is chaotic in the sense of Devaney and exhibits distributional chaos of type 1 with positive topological entropy.