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

Part of: Ergodic theory Topological dynamics

Published online by Cambridge University Press:  11 February 2019

DAVID BURGUET
DAVID BURGUET*
Affiliation:
LPMA - CNRS UMR 7599, Université Paris 6, 75252 Paris Cedex 05, France email david.burguet@upmc.fr
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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].

Keywords

entropyweak specificationuniversal systems

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification 37B99: None of the above, but in this section 37B10: Symbolic dynamics
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 8 , August 2020 , pp. 2098 - 2115
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Copyright
© Cambridge University Press, 2019

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