Chaos and complexity

In this paper we show how to relate a form of high-dimensional complexity t o chaotic and other types of dynamical systems. The derivation shows how "n ear-chaotic" complexity can arise without the presence of homoclinic tangle s or positive Lyapunov exponents. The relationship we derive follows from t he observation that the elements of invariant finite integer lattices of hi gh-dimensional dynamical systems can, themselves, be viewed as single integ ers rather than coordinates of a point in n-space. From this observation it is possible to construct high-dimensional dynamical systems which have pro perties of shifts but for which there is no conventional topological conjug acy to a shift. The particular manner in which the shift appears in high-di mensional dynamical systems suggests that some forms of complexity arise fr om the presence of chaotic dynamics which are obscured by the large dimensi onality of the system domain.