Simple Permutations, Pasting and Reversing.

Abstract

In this work, we will study a key result in Combinatorial Dynamics: the Sharkovskii Theorem. This theorem explains how periodic points are related in a map by genealogy. Then, we will explore simple permutations, since they are useful to show how forcing works in discrete dynamical systems. The works of Stefan, Berndhardt and AcostaHuma´nez about odd and power-of-two permutations will be studied, and finally, pasting and reversing techniques will be defined over permutations to state genealogy relationship over other orders.