| Volume 10, Number 6, 2020, Pages 2491-2505 DOI：10.11948/20190388 |
| Further discussion on Kato""s chaos in set-valued discrete systems |
| Risong Li,Tianxiu Lu,Guanrong Chen,Xiaofang Yang |
| Keywords:Kato""s chaos, collective accessibility, strongly accessible. |
| Abstract: |
| For a compact metric space $Y$ and a continuous map $g:Y\rightarrow Y$, the collective accessibility and collectively Kato chaotic of the dynamical system $(Y, g)$ were defined. The relations between topologically weakly mixing and collective accessibility, or strong accessibility, or strongly Kato chaos were studied. Some common properties of $g$ and $\overline{g}$ were given. Where $\overline{g}: \kappa(Y)\rightarrow \kappa(Y)$ is defined as $\overline{g}(B)=g(B)$ for any $B\in\kappa(Y)$, and $\kappa(Y)$ is the collection of all nonempty compact subsets of $Y$. Moreover, it is proved that $g$ is collectively accessible (or strongly accessible) if and only if $\overline{g}$ in $w^{e}$-topology is collectively accessible (or strongly accessible). |
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