Causality and state concepts in dynamical systems theory

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Abstract
The subject is considered in n general set-theoretic formalism. A time system is hero a set of ordered pairs of functions on a common time domain ; extensions to more general forms are also noted. A representation of a system S is an ‘ aggregate ’ of sets and structures by the aid of which each pair of S can be generated. Leading principles of the work arc : (i) Just a representation is a primarily interesting description of S, and it is a starting-point in analysis in most practical eases, (ii) Tbo concepts, like causality and state, are primarily defined as properties of representations. Three main forms of representations arc introduced : (i) (causal) parameter mapping ; (ii) state mapping ; and (iii) state transition mapping. The causality and state are here defined independently on each other. However, they turn out to be intimately connected via properties and interrelations of those forms, presented by some propositions. The aim of the work is to present an alternative formalism which is more closely connected with systems analysis in practice.

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