Integral rigid sets and periods of nonexpansive maps

AbstractFor ℓ1-norm and sup-norm nonexpansive maps it is known that bounded orbits approach periodic orbits. Moreover the minimal period of a periodic point of such a map has an a priori upper bound that only depends on the dimension and the given norm. We shall show that the question whether for a given positive integer p there exists an ℓ1-norm (or sup-norm) nonexpansive map f: Df → Df ⊂ R n with a periodic point of minimal period p can be answered in finite time