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arXiv · 2210.00115

A geometric framework for asymptoticity and expansivity in topological dynamics

Sebastián Donoso·Alejandro Maass·Samuel Petite
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Abstract

We develop a geometric framework to address asymptoticity and nonexpansivity in topological dynamics. Our framework can be applied when the acting group is second countable and locally compact. As an application, we show extensions of Schwartzman's theorem in this context. Also, we get new results when the acting groups is ${\mathbb Z}^d$: any half-space of ${\mathbb R}^d$ contains a vector defining a (oriented) nonexpansive direction in the sense of Boyle and Lind. Finally, we deduce rigidity properties of distal Cantor systems.

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Sebastián Donoso, Alejandro Maass, Samuel Petite. 2022-09-30. A geometric framework for asymptoticity and expansivity in topological dynamics. https://arxiv.org/abs/2210.00115

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