Abstract: We
consider discrete dynamical systems in the field
of p-adic numbers, for prime numbers We study systems that are given by iterations of
the monomial function where
is an integer. The dynamics looks totally
different whether or not. In both cases, the interesting
dynamics occurs on the unit sphere, in In this article, we describe the geometry and
algebraic properties of the dynamics on In order to get a clear description of these
properties, we introduce new concepts, such as,
periodic group, attractor group and l-shell.
We are able to calculate the number of fuzzy
cycles to the system. Some asymptotical results
are also found.
Keywords and phrases: p-adic dynamical systems, fuzzy cycles.
is an integer. The dynamics looks totally
different whether 
