Non-commuting, mixing, zero-entropy transformations can fail double recurrence along p1(n), p2(n) whenever the two polynomials are both linear or both have degree at least two.
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Counterexamples to double recurrence for non-commuting deterministic transformations
Non-commuting, mixing, zero-entropy transformations can fail double recurrence along p1(n), p2(n) whenever the two polynomials are both linear or both have degree at least two.