The least number, of n-periodic points of a self-map of a solvmanifold, can be realised by a smooth map

Shub and Sullivan noticed that there is a large gap between the least number of periodic points, taken over the family of continuous maps homotopic to a given self-map f and the analogous number taken over the family of smooth maps homotopic to f. In this paper we show that in the case of self-maps of solvmanifolds the minimal numbers of n-periodic points, in both categories, are equal.