On one polynomial $p$-adic dynamical system

TL;DR

This paper investigates the dynamical behavior of a specific polynomial $p$-adic system, focusing on its basin of attraction and Siegel discs over complex $p$-adic fields.

Contribution

It provides a detailed description of the basin of attraction and Siegel discs for the polynomial $p$-adic dynamical system $f(x)=x^{2n+1}+ax^{n+1}$ over complex $p$-adic fields, advancing understanding of such systems.

Findings

Characterization of basin of attraction

Description of Siegel discs

Analysis over complex $p$-adic fields

Abstract

In the paper we describe basin of attraction and the Siegel discs of the $p$-adic dynamical system $f(x)=x^{2n+1}+ax^{n+1}$ over complex $p$-adic field.