In this paper we establish that every (deterministic) non-autonomous, discrete-time, causal, time invariant system has a state-space representation, and discuss its minimality.

Time-discrete stochastic processes are powerful tools for characterizing some dynamical systems. The prerequisites include an understanding of Markov processes (13.1). Time-discrete systems behave quite differently from dynamical systems based on systems of ordinary differential equations. This chapter presents a Markov model of adaptive learning that illustrates the concept of stochastic stab...

In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.