Resumen de A p-adic behaviour of dynamical systems

Andrew Khrennikov, Stany de Smedt

• 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 cycles. 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...