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
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
Gleick  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 .
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.