Work

On dynamical parameter space of cubic polynomials with a parabolic fixed point

Year: 2024

Type: article

Abstract: This article focuses on the connectedness locus of the cubic polynomial slice with a parabolic fixed point of multiplier . We first show that any parabolic component, which is a parallel notion of hyperbolic component, is a Jordan domain. Moreover, a continuum called the central part in the connectedness locus is introduced. This is the natural analogue to the closure of the main hyperbolic component of . We prove that is almost a double covering of the filled‐in Julia set of the quadratic polynomial .

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70038

Author: Runze Zhang

Institution: Stony Brook University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4404921196

FWCI: 0.65

Cites: 28

Cited by: 3

Related to: 10