In [MS], we observe that combinatorial zeta functions whose determinant expressions are of the form 1/det(I-A) should be constructed as Ruelle zeta functions [R] for essentially finite

dynamical systems defined for finite digraphs.

sigma])> (in brief [phi]) is called a cocycle over the semigroup

dynamical system ([OMEGA], [Z.

Under the deterministic hypothesis, the

dynamical system is called autonomous, if the law L is invariant with time.

2000), "Random

Dynamical Systems in Economics," WP-67, Institute for Empirical Research in Economics, University of Zurich, December.

3]\D) is a trajectory of a potential

dynamical system with three degrees of freedom associated to the potential -f in int([R.

Parker is careful to point out that not every narrative benefits from the chaos theory, and the texts to which she applies the analogy in this study are carefully chosen for the ways in which they particularly exemplify aspects of a

dynamical systems theory.

Gleick [3] in his popular book on chaos, gives the views of several researchers: the complicated, aperiodic attracting orbits of certain

dynamical systems, apparently random recurrent behavior in a simple deterministic system, the irregular, unpredictable behavior of deterministic nonlinear

dynamical systems.

We thus illustrate precisely how physical laws in the classical regime of

dynamical systems fail to exhibit predictive power.

Haddad and Chel laboina view a

dynamical system as a precise mathematical object defined on a time set as a mapping between vector spaces satisfying a set of axioms.

17] The

dynamical system is said to converge to the solution set [K.

In contrast, each machine process is correct as a

dynamical system in its own right [6].

It is also important to point out that mathematically, it is in principle decidable whether a

dynamical system is stable or not, although in many cases it is a hard task in practice.