Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces

Let f be a smooth self-map of a closed connected manifold of dimension m ⩾ 3 . The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276–290] the topological invariant NJD r [ f ] , where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth self-maps of real projective space R P m , where m > 3 is odd, are considered and the estimations from below and above for NJD r [ f ] are given.