Sarnak's Möbius disjointness conjecture asserts that for any zero entropy dynamical system, for every and every. We construct examples showing that this can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of, one can put any bounded sequence such that the Cesàro mean of the corresponding sequence of absolute values does not tend to zero. Moreover, in our construction, the choice of x depends on the sequence anbut does not.
Bibliographical noteFunding Information:
We thank the anonymous referee for helpful comments. Z.W. was supported by NSF grant DMS-1753042. A. A. acknowledges support from the Hebrew University of Jerusalem, where some of this research was done.
© The Author(s), 2022. Published by Cambridge University Press.
- Möbius disjointness
- topological dynamics
- zero topological entropy
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics