Counterexamples to double recurrence for non-commuting deterministic transformations
Abstract
We show that if p1,p2 are injective, integer polynomials that vanish at the origin, such that either both are of degree 1 or both are of degree 2 or higher, then double recurrence fails for non-commuting, mixing, zero entropy transformations. This answers a question of Frantzikinakis and Host completely.
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