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Let  X  be a dendrite and letbe a continuous map that has an infinite minimal set  M  in  X . In the article we obtain conditions on the structure of a dendrite  X  and the set  M , under which  f  has an arc horseshoe, and, hence,  f  has a positive topological entropy. We show that this result is not correct both for continuous maps with an empty set of periodic points, and for continuous maps with a non-empty set of periodic points on finite graphs.

Remarks on minimal sets on dendrites and finite graphs