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Symbolic dynamics on amenable groups: the entropy of generic shifts

Frisch, Joshua and Tamuz, Omer (2015) Symbolic dynamics on amenable groups: the entropy of generic shifts. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20161111-134938105

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Abstract

Let G be a finitely generated amenable group. We study the space of shifts on G over a given finite alphabet A. We show that the zero entropy shifts are generic in this space, and that more generally the shifts of entropy c are generic in the space of shifts with entropy at least c. The same is shown to hold for the space of transitive shifts and for the space of weakly mixing shifts. As applications of this result, we show that for every entropy value c∈[0,log|A|] there is a weakly mixing subshift of A^G with entropy c. We also show that the set of strongly irreducible shifts does not form a G_δ in the space of shifts, and that all non-trivial, strongly irreducible shifts are non-isolated points in this space.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1503.06251arXivDiscussion Paper
ORCID:
AuthorORCID
Tamuz, Omer0000-0002-0111-0418
Additional Information:J. Frisch was supported by MIT’s Undergraduate Research Opportunities Program. This research was partially conducted at Microsoft Research, New England.
Funders:
Funding AgencyGrant Number
Massachusetts Institute of Technology (MIT)UNSPECIFIED
Record Number:CaltechAUTHORS:20161111-134938105
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161111-134938105
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71956
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Nov 2016 00:43
Last Modified:03 Oct 2019 16:12

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