Minimal number of periodic points for smooth self-maps of $S^3$
Let $f$ be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension $m\geq 3$ and $r$ a fixed natural number. A topological invariant $D^m_r[f]$, introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of $r$-periodic points for all smooth maps homotopic to $f$. In this paper we calculate $D^3_r[f]$ for all self-maps of $S^3$.