Relations between Escape Regions in the Parameter Space of Cubic Polynomials

2022/05/10 by Araceli Bonifant, Bonifant, Araceli, Chad Estabrooks +3
Mathematics · #37F10 #37F20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2205.04994

openalex publication_date 2022/05/10 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

Abstract

We describe a topological relationship between slices of the parameter space of cubic maps. In the paper \citeCP1, Milnor defined the curves S_n as the set of all cubic polynomials with a marked critical point of period p. In this paper, we will describe a relationship between the boundaries of the connectedness loci in the curves S₁ and S₂.

Related

• Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions
• Cubic Polynomial Maps with Periodic Critical Orbit, Part III: Tessellations and Orbit Portraits
• The geometry of the critically-periodic curves in the space of cubic polynomials
• Hyperbolic components of polynomials with a fixed critical point of maximal order
• Irreducibility of periodic curves in cubic polynomial moduli space