On the dynamics of the combinatorial model of the real line

Pedro J. Chocano

Published 2022-09-05Version 1

We study and classify the situations that arise in dynamical systems defined on the combinatorial model of the real line. Particularly, we prove that using single-valued maps there are no periodic points of period 3, which constrasts with the classical setting and proves that these maps are very restrictive. Then we use Vietoris-like multivalued maps to show that there is more flexibility, at least in terms of periods, in this combinatorial framework than in the usual one because we do not have the conditions about the existence of periods given by the Sharkovski Theorem.