Counterexamples to double recurrence for non-commuting deterministic transformations
Dynamical Systems
2025-07-22 v1
Abstract
We show that if are injective, integer polynomials that vanish at the origin, such that either both are of degree or both are of degree or higher, then double recurrence fails for non-commuting, mixing, zero entropy transformations. This answers a question of Frantzikinakis and Host completely.
Cite
@article{arxiv.2507.15528,
title = {Counterexamples to double recurrence for non-commuting deterministic transformations},
author = {Zemer Kosloff and Shrey Sanadhya},
journal= {arXiv preprint arXiv:2507.15528},
year = {2025}
}