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 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...
@article{urn:eudml:doc:44413,
title = {A p-adic behaviour of dynamical systems.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {12},
year = {1999},
pages = {301-323},
zbl = {0965.37067},
mrnumber = {MR1740462},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44413}
}
De Smedt, Stany; Khrennikov, Andrew. A p-adic behaviour of dynamical systems.. Revista Matemática de la Universidad Complutense de Madrid, Tome 12 (1999) pp. 301-323. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44413/