Geodesic
$p$-Adic dynamic systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 3, pp. 349-365

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Dynamic systems in non-Archimedean number fields (i. e. fields with non-Archimedean valuations) are studied. Results are obtained for the fields of $p$-adic numbers and complex $p$-adic numbers. Simple $p$-adic dynamic systems have a very rich structure–attractors, Siegel disks, cycles, and a new structure called a “fuzzy cycle”. The prime number $p$ plays the role of a parameter of the $p$-adic dynamic system. Changing $p$ radically changes the behavior of the system: attractors may become the centers of Siegel disks, and vice versa, and cycles of different lengths may appear or disappear. 
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     author = {S. A. Albeverio and B. Tirozzi and A. Yu. Khrennikov and S. de Smedt},
     title = {$p${-Adic} dynamic systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {349--365},
     publisher = {mathdoc},
     volume = {114},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_114_3_a2/}
}
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S. A. Albeverio; B. Tirozzi; A. Yu. Khrennikov; S. de Smedt. $p$-Adic dynamic systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 3, pp. 349-365. http://geodesic.mathdoc.fr/item/TMF_1998_114_3_a2/