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Let  be a smooth compact and simply-connected manifold with simply-connected boundary ,  be a fixed odd natural number. We consider , a  self-map of , preserving . Under the assumption that the dimension of  is at least 4, we define an invariant  that is equal to the minimal number of -periodic points for all maps preserving  and -homotopic to . As an application, we give necessary and sufficient conditions for a reduction of a set of -periodic points to one point in the -homotopy class.

Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds