Testing Conformity with Benford's Law in Chaotic Dynamical Systems

Benford's law, also known as the first digit law, gives a monotonically decreasing distribution of the first digit in the considered data set.Contrary to our intuition, which suggests that the first digit would appear with a uniform distribution, this is decreasingly logarithmic law, where the digit 1 is appearing with 30% chance and the digit 9 is appearing with 4.58% chance.The purpose of this paper is to consider whether the Benford's law can be applied on different dynamical systems (Lorenz, Hnon and Rssler).As a procedure, we analyze the frequency of the first and the second digit of the coordinates of the trajectories generated by these dynamical systems.We conclude that some trajectories follow Benford's law, while others do not, and some results depend of the choice of the parameters of the model.As the main point is that natural data generally follow Benford's law, we have shown that for some dynamical systems the distinction between the trajectories that follow Benford's law and that do not follow Benford's aw may be very small which may require much more careful consideration.