Tables of graphs of binary and ternary sequences differentiation

Abstract

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.

16 pages, 2 large tables, program on Mathematica

References in corpus (1)

• Multiplicative function instead of logarithm (an elementary approach)