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This article is cited in 45 scientific papers (total in 45 papers)
$p$-Adic dynamic systems
S. A. Albeverioa, B. Tirozzib, A. Yu. Khrennikovc, S. de Smedtd a University of Bonn, Institute for Applied Mathematics
b University of Rome "La Sapienza"
c Växjö University
d Vrije Universiteit
Abstract:
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.
Received: 28.08.1997
Citation:
S. A. Albeverio, B. Tirozzi, A. Yu. Khrennikov, S. de Smedt, “$p$-Adic dynamic systems”, TMF, 114:3 (1998), 349–365; Theoret. and Math. Phys., 114:3 (1998), 276–287
Linking options:
https://www.mathnet.ru/eng/tmf845https://doi.org/10.4213/tmf845 https://www.mathnet.ru/eng/tmf/v114/i3/p349
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