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Sarnak's conjecture for a class of rank-one subshifts.
- Source :
-
Proceedings of the American Mathematical Society, Series B . 12/19/2022, Vol. 9, p460-471. 12p. - Publication Year :
- 2022
-
Abstract
- Using techniques developed by Kanigowski, Lemańczyk, and Radziwiłł [Fund. Math. 255 (2021), pp. 309–336], we verify Sarnak's conjecture for two classes of rank-one subshifts with unbounded cutting parameters. The first class of rank-one subshifts we consider is called almost complete congruency classes (accc), the definition of which is motivated by the main result of Foreman, Gao, Hill, Silva, and Weiss [Isr. J. Math., To appear], which implies that when a rank-one subshift carries a unique nonatomic invariant probability measure, it is accc if it is measure-theoretically isomorphic to an odometer. The second class we consider consists of Katok's map and its generalizations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 23301511
- Volume :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society, Series B
- Publication Type :
- Academic Journal
- Accession number :
- 160869652
- Full Text :
- https://doi.org/10.1090/bproc/148