Geodesic
Symmetry of iteration graphs
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 131-145.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We examine iteration graphs of the squaring function on the rings $\mathbb{Z}/n\mathbb{Z}$ when $n = 2^{k}p$, for $p$ a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when $k=3$ and when $k\ge 5$ and are symmetric when $k = 4$.
Classification : 05C20, 05C62, 11T99
Keywords: digraph; iteration digraph; quadratic map; tree; cycle 
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     title = {Symmetry of iteration graphs},
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     zbl = {1174.05048},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2008__58_1_a8/}
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Carlip, Walter; Mincheva, Martina. Symmetry of iteration graphs. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 131-145. http://geodesic.mathdoc.fr/item/CMJ_2008__58_1_a8/