,
in general fractal one. The exact value of
is the
limit of the sequence of 
and the IFS generated the hyperreal
number. The Kolmogorov and Sinai entropy (KSE) of IFS is the exact
value of hyperreal number, and the Rényi entropy is equal to
the topological entropy. The KSE is the limit case of Rényi
entropy and the halo of monad can be represented as the difference
between these entropies. For two - dimensional Markov processes
the halo of monad is represented as hypersphere in index space.
For a social hierarchical dynamical system the increasing of
indeterminacy by the system growth is found. This increasing is a
function of the operators of hierarchical movements
and
.
Key words: dynamical system, iterated function system, hierarchy, non-standard analysis, entropy, monad, haziness, indeterminacy
