Least number of n-periodic points of self-maps of PSU(2)times PSU(2)

Abstract

Let f:Mrightarrow M be a self-map of a compact manifold and nin {mathbb {N}}. In general, the least number of n-periodic points in the smooth homotopy class of f may be much bigger than in the continuous homotopy class. For a class of spaces, including compact Lie groups, a necessary condition for the equality of the above two numbers, for each iteration f^n, appears. Here we give the explicit form of the graph of orbits of Reidemeister classes mathcal {GOR}(f^*) for self-maps of projective unitary group PSU(2) and of PSU(2)times PSU(2) satisfying the necessary condition. The structure of the graphs implies that for self-maps of the above spaces the necessary condition is also sufficient for the smooth minimal realization of n-periodic points for all iterations.