Iterated maps with exponential slopes for nonlinear dynamics generation

The purpose of this paper is to analyze the theoretical feasibility of several classes of iterated maps with specified, desired properties, to help design the feasible ones, and further investigate some of their properties. As the main theoretical result, we establish some feasibility conditions for iterated maps suitable for the implementation on microsystems. The topic intimately relates to exponential Diophantine equations, namely to the new type represented by equation, with variables t
_k
and x
_k
.