Minimal number of periodic points for smooth self-maps of \(\mathbb {R}P^3\) (Q975229)

Suppose that \(M\) is a compact manifold. The lower bound for the number of \(r\)-periodic fixed points in the homotopy class of \(f\) is \[ NF_r(f)=\min\{\# \text{Fix}(g^r)\;g\simeq f\}. \] The authors study the counterpart of \(NF_r(f)\) in the smooth category, denoted by \(NJD_r[f]\). In particular, they determine \(NJD_r[f]\) for the real projective space, \(M={\mathbb R} P^3\). If \(\deg (f)\) is even or when \(\deg (f)\) is odd and \(r\) is odd, the problem can be reduced to the simply connected case. If \(\deg (f)\) is odd and \(r\) is even, the results are more complicated.