On Dynamical Parameter Space of Cubic Polynomials with a Parabolic Fixed Point

2022/11/22 by Zhang, Runze · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.12537

Abstract

This article focus on the connected locus of the cubic polynomial slice Per₁(λ) with a parabolic fixed point of multiplier λ=e^2πi(p)/(q). We first show that any parabolic component, which is a parallel notion of hyperbolic component, is a Jordan domain. Moreover, a continuum K_λ called the central part in the connected locus is defined. This is the natural analogue to the closure of the main hyperbolic component of Per₁(0). We prove that K_λ is almost a double covering of the filled-in Julia set of the quadratic polynomial P_λ(z) = λz+z².

Cited by

• Arithmetic Geometric Model for the Renormalisation of Bi-critical Irrationally Indifferent Attractors
• Parabolic Implosion in the Parameter Space of Cubic Polynomials

Related

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