Open Research Index

Auslander–Yorke dichotomy for minimal metric maps

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

Palomar Registrypalomar/PALOMAR-2026-10-29-000037Oct 29, 2026math.DSscore 0

For a continuous map of a metric space with every forward natural orbit dense, either the map is sensitive in the open-set pair sense or its natural iterate family is equicontinuous at every point. Stable open sets are propagated using dense orbits and finite early-time continuity. On nonempty spaces nonsensitivity is equivalent to equicontinuity; no compactness or uniform-equicontinuity assertion is required.

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