Publication Date
2022
Document Type
Article
Organizational Units
College of Natural Science and Mathematics, Mathematics
Keywords
Symbolic dynamics, Word complexity, Strong mixing, Rank-one transformations
Abstract
We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any f : N → N with f (n)/n increasing and ∑ 1/f (n) < ∞, that there exists an extremely elevated staircase with word complexity p(n) = o(f (n)). This improves the previously lowest known complexity for mixing subshifts, resolving a conjecture of Ferenczi.
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Statement
This article was originally published as:
Creutz, D., Pavlov, R., & Rodock, S. (2022). Measure-theoretically mixing subshifts with low complexity. Ergodic Theory and Dynamical Systems, 1-24. doi:10.1017/etds.2022.42
Copyright is held by the authors. User is responsible for all copyright compliance.
Rights Holder
Darren Creutz, Ronnie Pavlov, Shaun Rodock
Provenance
Received from author
File Format
application/pdf
Language
English (eng)
Extent
24 pgs
File Size
413 KB
Publication Title
Ergodic Theory and Dynamical Systems
Volume
43
First Page
1
Last Page
24
Recommended Citation
Creutz, Darren; Pavlov, Ronnie; and Rodock, Shaun, "Measure-theoretically Mixing Subshifts with Low Complexity" (2022). Mathematics: Faculty Scholarship. 57.
https://digitalcommons.du.edu/math_faculty/57
https://doi.org/10.1017/etds.2022.42
DOI Link
https://doi.org/10.1017/etds.2022.42
