The aim of the present paper is to study the dynamics of a class of
orbitally continuous non-linear mappings defined on the set of real numbers
and to apply the results on dynamics of functions to obtain tests of
divisibility. We show that this class of mappings contains chaotic mappings.
We also draw Julia sets of certain iterations related to multiple lowering
mappings and employ the variations in the complexity of Julia sets to
illustrate the results on the quotient and remainder. The notion of orbital
continuity was introduced by Lj. B. Ciric and is an important tool in
establishing existence of fixed points.
On the convergence of an iteration method for continuous mappings on an arbitrary interval
