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

U. A. Rozikov

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

Dynamical Systems 2021-01-15 v1

Authors: U. A. Rozikov

Abstract

In this paper we study $p$ -adic dynamical systems generated by the function $f(x)={a\over x^2}$ in the set of complex $p$ -adic numbers. We find an explicit formula for the $n$ -fold composition of $f$ for any $n\geq 1$ . 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 $a$ .

Keywords

p-adic analysis dynamical systems and chaos p-adic hodge theory

Cite

@article{arxiv.2101.05750,
  title  = {$p$-adic dynamical systems of the function $a x^{-2}$},
  author = {U. A. Rozikov},
  journal= {arXiv preprint arXiv:2101.05750},
  year   = {2021}
}

Comments

11 pages

Related papers

View all related →