Abstract

In this paper we obtain a characterization of $k$-type
transitivity for a $\mathbb{Z}^d$-action on certain spaces and
then prove that $k$-type SDIC is redundant in the definition of
$k$-type Devaney chaos for $\mathbb{Z}^d$-actions on infinite
metric spaces. We define different types of chaos for
$\mathbb{Z}^d$-actions and prove results related to their
preservations under conjugacy and uniform conjugacy. Finally we
discuss $k$-type properties on product spaces.

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