$$p$$-Adic Dynamical Systems of the Function $$a x^{-2}$$

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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