Topological and almost Borel universality for systems with the weak specification property

David Burguet

doi:10.1017/etds.2019.7

Topological and almost Borel universality for systems with the weak specification property

David Burguet

École Polytechnique

Research output: Contribution to journal › Article › peer-review

Abstract

We show that systems with some specification properties are topologically or almost Borel universal, in the sense that any aperiodic subshift with lower entropy may be topologically or almost Borel embedded. This improves, with elementary tools, previous results of Quas and Soo [Ergodic universality of some topological dynamical systems. Trans. Amer. Math. Soc.368 (2016), 4137-4170].

Original language	English
Pages (from-to)	2098-2115
Number of pages	18
Journal	Ergodic Theory and Dynamical Systems
Volume	40
Issue number	8
DOIs	https://doi.org/10.1017/etds.2019.7
Publication status	Published - 1 Aug 2020

Keywords

Entropy
Universal systems
Weak specification

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10.1017/etds.2019.7

Cite this

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abstract = "We show that systems with some specification properties are topologically or almost Borel universal, in the sense that any aperiodic subshift with lower entropy may be topologically or almost Borel embedded. This improves, with elementary tools, previous results of Quas and Soo [Ergodic universality of some topological dynamical systems. Trans. Amer. Math. Soc.368 (2016), 4137-4170].",

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AB - We show that systems with some specification properties are topologically or almost Borel universal, in the sense that any aperiodic subshift with lower entropy may be topologically or almost Borel embedded. This improves, with elementary tools, previous results of Quas and Soo [Ergodic universality of some topological dynamical systems. Trans. Amer. Math. Soc.368 (2016), 4137-4170].

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KW - Weak specification

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DO - 10.1017/etds.2019.7

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JO - Ergodic Theory and Dynamical Systems

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Topological and almost Borel universality for systems with the weak specification property

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Keywords

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