Sharkovsky's Theorem and one-dimensional combinatorial dynamics

TL;DR

This paper provides an elementary proof of Sharkovsky's Theorem and explores its generalization to maps on graphs, serving as an accessible introduction to one-dimensional combinatorial dynamics.

Contribution

It offers a new elementary proof of Sharkovsky's Theorem and extends the theorem to graph maps, broadening its applicability.

Findings

Elementary proof of Sharkovsky's Theorem

Generalization to graph maps

Introduction to one-dimensional combinatorial dynamics

Abstract

A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is written at an elementary level and is meant as an introduction to one-dimensional combinatorial dynamics.