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Furstenberg weak mixing and finite diagonal powers

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-28-000033Oct 28, 2026math.DSscore 0

For a continuous self-map of a nonempty topological space, square transitivity implies transitivity of every finite diagonal power, including power zero. A genuine open-pair refinement and finite induction give a common natural forward hitting time for any finite family of nonempty open pairs. The literal two-pair condition is proved equivalent to actual square transitivity.

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