p-adic dynamical systems of the function a x^-2

2021/01/14 by U. A. Rozikov, Rozikov, U. A.
Mathematics · #37P05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2101.05750

openalex publication_date 2021/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study p-adic dynamical systems generated by the function f(x)=a\over x² in the set of complex p-adic numbers. We find an explicit formula for the n-fold composition of f for any n≥ 1. Using this formula we give fixed points, periodic points, basin of attraction and Siegel disk of each fixed (periodic) point depending on parameters p and a.

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