Devaney’s chaos implies distributional chaos in a sequence |
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Authors: | Heng Liu Lidong Wang Zhenyan Chu |
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Institution: | Department of Mathematics, Dalian Nationalities University, 116600, PR China |
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Abstract: | Let X be a complete metric space without isolated points, and let f:X→X be a continuous map. In this paper we prove that if f is transitive and has a periodic point of period p, then f is distributionally chaotic in a sequence. Particularly, chaos in the sense of Devaney is stronger than distributional chaos in a sequence. |
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Keywords: | Devaney&rsquo s chaos Distributional chaos in a sequence Transitivity |
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