P-ADIC DYNAMIC-SYSTEMS

Dynamic systems in non-Archimedean number fields (i.e., fields with no n-Archimedean valuations) are studied. Results are obtained for the fi elds of p-adic numbers and complex p-adic numbers. Simple p-adic dynam ic systems have a very rich structure-attractors, Siegel disks, cycles , and a new structure called a ''fuzzy cycle.'' The prime number p pla ys the role of a parameter of the p-adic dynamic system. Changing p ra dically changes the behavior of the system: attractors may become the centers of Siegel disks, and vice versa, and cycles of different lengt hs may appear or disappear.