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In this note we give examples of Hamiltonian diffeomorphisms which are on onehand dynamically complicated, for instance with positive topological entropy,and on the other hand minimal from the perspective of Floer theory. Theminimality is in the sense that the barcode of the Floer complex of alliterates of these maps consists of only infinite bars. In particular, the mapshave zero barcode entropy.

A generalized pseudo-rotation with positive topological entropy