Full paper in PDF:
$%S. De Smedt and A. Khrennikov, A p-adic behavior of dynamical systems,
Rev. Mat. Complut. 12 (1999), no. 2, 301–323.%$
Faculty of Applied Sciences Vrije Universiteit Brussel Pleinaan 2 1050 Brussel — Belgium | Department of Mathematics Rikkyo University Ikebukuro, Toshima-ku Tokyo 171 — Japan |
ABSTRACT
We study dynamical systems in the non-Archimedean number fields (i.e., fields with non-Archimedean valuation). The main results are obtained for the fields of -adic numbers and complex -adic numbers. Already the simplest -adic dynamical systems have a very rich structure. There exist attractors, Siegel disks and cycles. There also appear new structures such as “fuzzy cycles.” A prime number plays the role of parameter of a dynamical system. The behavior of the iterations depends on this parameter very much. In fact, by changing p we can change crucially the behavior: attractors may become centers of Siegel disks and vice versa, cycles of different length may appear and disappear…
1991 Mathematics Subject Classification: 46S10, 58F12.