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In [30] different statistical behavior of dynamical orbits without syndeticcenter are considered. In present paper we continue this project and considerdifferent statistical behavior of dynamical orbits with nonempty syndeticcenter: Two of sixteen cases appear (for which other fourteen cases are stillunknown) in transive topologically expanding or hyperbolic systems and arediscovered to have full topological entropy for which it is also true ifcombined with non-recurrence and multifractal analysis such as quasi-regularset, irregular set and level sets. In this process a strong entropy-denseproperty, called minimal-entropy-dense, is established. In particular, we showthat points that are minimal (or called almost periodic), a classical andimportant concept in the study of dynamical systems, form a set with fulltopological entropy if the dynamical system satisfies shadowing or almostspecification property.

Different Statistical Future of Dynamical Orbits over Expanding or Hyperbolic Systems (II): Nonempty Syndetic Center