Geodesic
On some issues concerning polynomial cycles
Communications in Mathematics, Tome 21 (2013) no. 2, pp. 129-135.

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We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain $R$ of positive characteristic (for $N\ge 1$) or for any Dedekind domain $R$ of positive characteristic (but only for $N\ge 2$), we give a closed formula for a set ${\cal CYCL}(R,N)$ of all possible cycle-lengths for polynomial mappings in $R^N$. Then we give a new property of sets ${\cal CYCL}(R,1)$, which refutes a kind of conjecture posed by W. Narkiewicz.
Classification : 11R09, 13F05, 37P35
Keywords: polynomial cycles; discrete valuation domains; Dedekind rings 
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Pezda, Tadeusz. On some issues concerning polynomial cycles. Communications in Mathematics, Tome 21 (2013) no. 2, pp. 129-135. http://geodesic.mathdoc.fr/item/COMIM_2013__21_2_a2/