  In [30] different statistical behavior of dynamical orbits without syndetic
center are considered. In present paper we continue this project and consider
different statistical behavior of dynamical orbits with nonempty syndetic
center: Two of sixteen cases appear (for which other fourteen cases are still
unknown) in transive topologically expanding or hyperbolic systems and are
discovered to have full topological entropy for which it is also true if
combined with non-recurrence and multifractal analysis such as quasi-regular
set, irregular set and level sets. In this process a strong entropy-dense
property, called minimal-entropy-dense, is established. In particular, we show
that points that are minimal (or called almost periodic), a classical and
important concept in the study of dynamical systems, form a set with full
topological entropy if the dynamical system satisfies shadowing or almost
specification property.
