Geodesic
$p$-Adic Entropies of Logistic Maps
Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 257-263

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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. 
@article{TRSPY_2004_245_a25,
     author = {G. B. Shabat},
     title = {$p${-Adic} {Entropies} of {Logistic} {Maps}},
     journal = {Informatics and Automation},
     pages = {257--263},
     publisher = {mathdoc},
     volume = {245},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a25/}
}
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G. B. Shabat. $p$-Adic Entropies of Logistic Maps. Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 257-263. http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a25/