Sharkovsky's Ordering in the Mandelbrot Set

2025/06/06 by Zheng, Reila
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Chaos control and synchronization #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2506.06163

openalex publication_date 2025/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sharkovsky's ordering describes orbit forcing of interval maps, and generalizations of Sharkovsky's ordering exist for maps of trees. In this paper I will describe Sharkovsky's ordering and analogous orderings for trees, and their occurrence on the Mandelbrot set.

Citations

• Periodic Orbits, Externals Rays and the Mandelbrot Set: An Expository Account
• Internal addresses in the Mandelbrot set and Galois groups of polynomials

Related

• A partial order on Motzkin paths
• Universal functions for the Sharkovsky classes of maps
• Broad posets, trees, and the dendroidal category
• Mandelbulb, Mandelbrot, Mandelring and Hopfbrot
• Sharkovsky's Theorem and one-dimensional combinatorial dynamics