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arXiv · 2304.02073

Strong topological transitivity, hypermixing, and their relationships with other dynamical properties

Ian Curtis·Sean Griswold·Abigail Halverson·Eric Stilwell·Sarah Teske·David Walmsley·Shaozhe Wang
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Abstract

Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger version of the mixing property. We continue the investigation of these notions with two main results. First, we show there are dynamical systems which are strongly topologically transitive but not weakly mixing. We then show that on $\ell^p$ or $c_0$, there is a weighted backward shift which is strongly topologically transitive but not mixing.

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Ian Curtis, Sean Griswold, Abigail Halverson, Eric Stilwell, Sarah Teske, David Walmsley, Shaozhe Wang. 2023-04-04. Strong topological transitivity, hypermixing, and their relationships with other dynamical properties. https://arxiv.org/abs/2304.02073

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