$p$-Adic Entropies of Logistic Maps
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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{TM_2004_245_a25,
author = {G. B. Shabat},
title = {$p${-Adic} {Entropies} of {Logistic} {Maps}},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {257--263},
year = {2004},
volume = {245},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_2004_245_a25/}
}
G. B. Shabat. $p$-Adic Entropies of Logistic Maps. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 257-263. http://geodesic.mathdoc.fr/item/TM_2004_245_a25/
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