Approximately-finite memory and discrete-time input-output maps

A body of results is given concerning the character of the response of syst ems represented by discrete-time approximately-finite-memory input-output m aps G with input and outputs defined on {0, 1,...}. Conditions are given un der which, for example, the system's output approaches a limit as k -->infi nity whenever the input does. Of particular interest are theorems that conc ern the existence and properties of a certain unique extension of G to a co rresponding domain of functions defined on all of {..., -1, 0, 1...}. The t heorems lead to a general proposition that characterizes the response of a very large class of non-linear systems to asymptotically periodic inputs. C opyright (C) John Wiley & Sons, Ltd.