$p$-Adic Entropies of Logistic Maps

We study the dynamic properties of the logistic maps $x\to\lambda x(1-x)$ over the fields of $p$-adic numbers. We are interested in the chaotic behavior of trajectories; it turns out that, for a fixed rational $\lambda$, such behavior occurs only for finitely many $p$'s. This fact is consistent with the main result of the paper: the calculation of topological entropies of these maps. The possibility of the adelic interpretation of this result is discussed.