For a class I was teaching, I was demonstrating time-series analysis with the famous discrete-time dynamical system $x_{n+1} = ax_n(1-x_n)$, where $a = 4 - \epsilon$ ($\epsilon$ ``small'') and different initial values of $x_0$.

When looking at the tenths digits of the numbers in the orbit $x_0, x_1, x_2, \ldots$, there was a strong bias towards "0" and "9" over the other digits. This was consistent across a wide range of $x_0$ and $\epsilon$, even though the orbits otherwise appeared to be pure noise,

Is this some numerical/computational phenomenon, or is it actually mathematically valid? In other words, are there results in the literature about the distribution of certain digits in chaotic orbits?

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