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arXiv · 2101.05750

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

U. A. Rozikov
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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 $a$.

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U. A. Rozikov. 2021-01-14. $p$-adic dynamical systems of the function $a x^{-2}$. https://arxiv.org/abs/2101.05750

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