Geodesic
Qualitative theory of $p$-adic dynamical systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 2, pp. 220-229

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We consider a class of dynamical systems over the $p$-adic number field: hierarchical dynamical systems. We prove a strong variant of the Poincaré theorem on the number of returns for such systems and show that hierarchical systems do not admit mixing. We describe hierarchical dynamical systems over the projective line and present an example of a nonhierarchical $p$-adic system that admits mixing: the $p$-adic baker's transformation.
Keywords: $p$-adic dynamical system, ergodicity, mixing, $p$-adic baker's transformation. 
@article{TMF_2014_178_2_a1,
     author = {E. I. Zelenov},
     title = {Qualitative theory of $p$-adic dynamical systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {220--229},
     publisher = {mathdoc},
     volume = {178},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_178_2_a1/}
}
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E. I. Zelenov. Qualitative theory of $p$-adic dynamical systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 2, pp. 220-229. http://geodesic.mathdoc.fr/item/TMF_2014_178_2_a1/