  Let $x$ be a cyclic sequence of $n$ elements of the finite field
$\mathbb{F}_q$ (the first element immediately follows the $n$-th one). Let us
define the operation $\Delta$ as the transition from $x$ to the sequence of
differences of the neighbouring elements from $x$. The aim of this work is to
give graphs of the dynamic system $\Delta$ for $q=2$, $n\le 300$ and $q=3$,
$n\le 150$. These results enable us to define more precisely the Arnold
hypotheses and to prove them.
