For EDITORS

For READERS

All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
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).