Linearizability of cubic polynomials at irrationally indifferent fixed points

TL;DR

This paper investigates the linearizability of cubic polynomials at irrationally indifferent fixed points, focusing on the complex dynamics and conditions under which such polynomials can be linearized.

Contribution

The paper introduces a refined approach to analyze linearizability of cubic polynomials at irrationally indifferent fixed points, emphasizing the role of additional parameters.

Findings

Linearizability depends on specific arithmetic conditions.

New estimates for the function $h^{*}_{n}(b,A)$ are proposed.

Further research is needed to fully characterize the parameter space.

Abstract

This paper has been withdrawn by the authors due to a more research needed to estimate $h^{*}_{n}(b)$ which really should be written as $h^{*}_{n}(b,A)$ for $b\in \Gamma (t)$.