Behavior of a class of nonlinear discrete-time systems (Q1090296)

A novel collection of nonlinear discrete-time systems is analyzed and characterized up to isomorphism. The systems in question are autonomous and deterministic and have the half-open unit interval [0,1) as state space. The analysis establishes isomorphisms between these systems and the members of an especially simple, easy-to understand, normal-form subclass of ''prototype'' systems. The prototypes consist exclusively of piecewise-linear systems with parallel pieces. The theory hinges upon a generally unfamiliar but remarkable real number representation resembling ordinary binary or decimal notation but involving a radix or base which is not an integer.