Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
Consider the family of self maps \(f: M\to M\) of a compact simply-connected manifold of dimension greater or equal to 4, whose boundary is simply-connected as well. Given an odd natural number \(r\), this paper describes an invariant that associates to \(f\) the minimal number of \(r\)-periodic orbits for all maps over the \(C^1\)-homotopy class of \(f\) that preserve the boundary of \(M\). Necessary and sufficient conditions for the reduction of a set of \(r\)-periodic points to one in the \(C^1\)-homotopy class are given as application.
scientific article; zbMATH DE number 6705655
scientific article