Geodesic
$p$-Adic Monomial Dynamical Systems
Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 202-209

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We consider discrete dynamical systems in the field of $p$-adic numbers, $\mathbb{Q}_p$, for prime numbers $p\geq 3$. We study systems that are given by iterations of the monomial function $x\mapsto x^n$, where $n\geq 2$ is an integer. The dynamics looks totally different depending on whether ${p\mid n}$ or not. In both cases, interesting dynamics occurs on the unit sphere, $S_1(0)$ in $\mathbb {Q}_p$. In this article, we state some results about cycles and fuzzy cycles. 
@article{TRSPY_2004_245_a19,
     author = {M. Nilsson},
     title = {$p${-Adic} {Monomial} {Dynamical} {Systems}},
     journal = {Informatics and Automation},
     pages = {202--209},
     publisher = {mathdoc},
     volume = {245},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a19/}
}
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M. Nilsson. $p$-Adic Monomial Dynamical Systems. Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 202-209. http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a19/