Slices of Parameter Space of Cubic Polynomials
Alexander Blokh, Lex Oversteegen, Vladlen Timorin

TL;DR
This paper investigates specific slices of the parameter space of cubic polynomials, focusing on the main cubioid and its properties related to fixed points and dynamical behavior.
Contribution
It characterizes the location of the main cubioid within these parameter slices, extending understanding of cubic polynomial dynamics.
Findings
Identification of the main cubioid in parameter space
Analysis of the dynamical properties of cubic polynomials
Insights into the structure of polynomial parameter spaces
Abstract
In this paper, we study slices of the parameter space of cubic polynomials, up to affine conjugacy, given by a fixed value of the multiplier at a non-repelling fixed point. In particular, we study the location of the in this parameter space. The is the set of affine conjugacy classes of complex cubic polynomials that have certain dynamical properties generalizing those of polynomials for in the filled main cardioid.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Mathematical Dynamics and Fractals · Advanced Topics in Algebra
