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Register a new userAlmost strong mixing group actions in topological dynamics
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Jane Wang
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In ergodic theory, given sufficient conditions on the system, every weak mixing $mathbb{N}$-action is strong mixing along a density one subset of $mathbb{N}$. We ask if a similar statement holds in topological dynamics with density one replaced with thickness. We show that given sufficient initial conditions, a group action in topological dynamics is strong mixing on a thick subset of the group if and only if the system is $k$-transitive for all $k$, and conclude that an analogue of this statement from ergodic theory holds in topological dynamics when dealing with abelian groups.
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