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Generic chaos on dendrites
Ergodic Theory and Dynamical Systems ( IF 0.9 ) Pub Date : 2021-03-19 , DOI: 10.1017/etds.2021.10
ĽUBOMÍR SNOHA 1 , VLADIMÍR ŠPITALSKÝ 2 , MICHAL TAKÁCS 1
Affiliation  

We characterize dendrites D such that a continuous selfmap of D is generically chaotic (in the sense of Lasota) if and only if it is generically ${\varepsilon }$ -chaotic for some ${\varepsilon }>0$ . In other words, we characterize dendrites on which generic chaos of a continuous map can be described in terms of the behaviour of subdendrites with non-empty interiors under iterates of the map. A dendrite D belongs to this class if and only if it is completely regular, with all points of finite order (that is, if and only if D contains neither a copy of the Riemann dendrite nor a copy of the $\omega $ -star).



中文翻译:

树突上的一般混乱

我们刻画树突D使得 D 的连续自映射一般是混沌的(在 Lasota意义上)当且仅当它对于某些 ${\varepsilon }>0$ 是一般的 ${\varepsilon }$ -混沌。换句话说,我们描述了树突,在这些树突上,连续映射的一般混沌可以根据映射迭代下具有非空内部的子树突的行为来描述。一个树突D属于这个类当且仅当它是完全正则的,并且所有点都是有限阶的(也就是说,当且仅当D既不包含黎曼树突的副本也不包含 $\omega $ -star的副本)。

更新日期:2021-03-19
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