Infinite realizations of an ``input-output'' mapping with continuous time (Q1921536)

The purpose of the present paper is to describe the evolutional (semigroup) properties of the internal dynamics of an abstract dynamic system. Infinite-dimensional realizations of an input-output mapping with continuous time for abstract dynamic systems are found. The author investigates canonical decompositions of these mappings, evolutional description for abstract nonpredicting systems and connection between the cause-and-effect and evolutional descriptions. The transfer function is replaced by a functional relationship between the prehistories and histories of segments of the dynamic processes. The structure of a system is determined by the proposed algorithm of the change. In particular, it is not necessary for the dynamic processes in the system to be described by ordinary differential equations.