Frisch, Joshua and Tamuz, Omer (2015) Symbolic dynamics on amenable groups: the entropy of generic shifts. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20161111-134938105
![]() |
PDF
- Submitted Version
See Usage Policy. 292Kb |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20161111-134938105
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: |
| ||||||
ORCID: |
| ||||||
Additional Information: | J. Frisch was supported by MIT’s Undergraduate Research Opportunities Program. This research was partially conducted at Microsoft Research, New England. | ||||||
Funders: |
| ||||||
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 |
Repository Staff Only: item control page