A generalized pseudo-rotation with positive topological entropy

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