A natural family of factors for product $\mathbb{Z}^2$-actions
Keywords
Topological dynamics, structure of factors, natural families of factorsAbstract
It is shown that if ${\mathcal N}$ and ${\mathcal N}'$ are natural families of factors (in the sense of [E. Glasner, M. K. Mentzen and A. Siemaszko, < i> A natural family of factors for minimal flows< /i> , Contemp. Math. < b> 215< /b> (1998), 19–42]) for minimal flows $(X,T)$ and $(X',T')$, respectively, then $\{R\otimes R'\colon R\in{\mathcal N},R'\in{\mathcal N}'\}$ is a natural family of factors for the product $\mathbb{Z}^2$-action on $X\times X'$ generated by $T$ and $T'$. An example is given showing the existence of topologically disjoint minimal flows $(X,T)$ and $(X',T')$ for which the family of factors of the flow $(X\times X',T\times T')$ is strictly bigger than the family of factors of the product $\mathbb{Z}^2$-action on $X\times X'$ generated by $T$ and $T'$. There is also an example of a minimal distal system with no nontrivial compact subgroups in the group of its automorphisms.Downloads
Published
2008-09-01
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SIEMASZKO, Artur. A natural family of factors for product $\mathbb{Z}^2$-actions. Topological Methods in Nonlinear Analysis. Online. 1 September 2008. Vol. 32, no. 1, pp. 187 - 197. [Accessed 20 April 2024].
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