Chaotic Dynamics of Composition Operators on the Space of Continuous Functions

被引：4
|
作者：
Yin, Zongbin [1 ]
机构：
[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 06期
关键词：
Devaney chaos; distributional chaos; frequent hypercyclicity; composition operators; DISTRIBUTIONAL CHAOS;
D O I：
10.1142/S0218127417500845
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the chaotic dynamics of composition operators on the space of real-valued continuous functions is investigated. It is proved that the hypercyclicity, topologically mixing property, Devaney chaos, frequent hypercyclicity and the specification property of the composition operator are equivalent to each other and are stronger than dense distributional chaos. Moreover, the composition operator C-phi exhibits dense Li-Yorke chaos if and only if it is densely distributionally chaotic, if and only if the symbol phi admits no fixed points. Finally, the long-time behaviors of the composition operator with affine symbol are classified in detail.
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页数：12
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