Sharkovsky's Theorem and one-dimensional combinatorial dynamics

2012/01/17 by Chris Bernhardt, Bernhardt, Chris
Mathematics · Physics and Astronomy · #05C50 #37E15 #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1201.3583

openalex publication_date 2012/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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