Two Counterexamples to a Conjecture by Agronsky and Ceder

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A conjecture by Agronsky and Ceder [3], stating that a continuum is an orbit enclosing ω-limit set of a continuous map from the k-dimensional cube Ik into itself if and only if it is arcwise connected, is disproved in both directions. Our main result is a general theorem allowing a construction of orbit enclosing ω-limit sets for triangular maps.

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