Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realizing ergodic properties in zero entropy subshifts   A subshift with linear block complexity has at most countably many ergodic
measures, and we continue of the study of the relation between such complexity
and the invariant measures. By constructing minimal subshifts whose block
complexity is arbitrarily close to linear but has uncountably many ergodic
measures, we show that this behavior fails as soon as the block complexity is
superlinear. With a different construction, we show that there exists a minimal
subshift with an ergodic measure whose slow entropy grows slower than any given
rate tending to infinitely but faster than any other rate majorizing this one
yet still growing subexponentially. These constructions lead to obstructions in
using subshifts in applications to properties of the prime numbers and in
finding a measurable version of the complexity gap that arises for shifts of
sublinear complexity.

22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys