Forcing of periodic orbits for interval maps and renormalization of piecewise affine maps

Abstract

We prove that for continuous maps on the interval, the existence of an n n -cycle implies the existence of n − 1 n-1 points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise affine maps (with no zero slope) cannot be infinitely renormalizable.