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 p-adic numbers and complex p-adic numbers. Already the simplest p-adic dynamical systems have a very rich structure.There exist attractors, Siegel disks and There also appear new structures such as fuzzy cycles. A prime number p plays the role of parameter of a dynamical system. The behaviour of the iterations depends on this parameter very much. In fact, by changing p we can change crucially the behaviour: attractors may become centers of Siegel disks and vice versa, cycles of different length may appear and disappear...
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