  Empirically defining some constant probabilistic orbits of f(x) and g(x)
iterated high-order functions, the stability of these functions in possible
entangled interaction dynamics of the environment through its orbit's
connectivity (open sets) provides the formation of an exponential dynamic fixed
point b = S(n+1) as a metric space (topological property) between both iterated
functions for short time lengths. However, the presence of a dynamic fixed
point f(g(x)) (x+1) can identify a convergence at iterations for larger time
lengths of b (asymptotic stability in Lyapunov sense). Qualitative (QDE)
results show that the average distance between the discontinuous function g(x)
to the fixed point of the continuous function f(x) (for all possible
solutions), might express fluctuations of g(x) on time lengths (instability
effect). This feature can reveal the false empirical asymptotic instability
behavior between the given domains f and g due to time lengths observation and
empirical constraints within a well-defined Lyapunov stability.
