Polynomial-like semi-conjugates of the shift map

2009/12/21 by Carsten Lunde Petersen, Petersen, Carsten Lunde
Mathematics · #37F10 #37F20 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0912.4181

openalex publication_date 2009/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper I prove that for a polynomial of degree d with a Cantor Julia set J, the Julia set can be understood as the simplest possible quotiont of the one sided shift space Σ_d with dynamics given by the shift. Here simplest possible means that, the projection π: Σ_d ⇒ J is as injective as possible.

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