  In this article we mainly aim to know what kind of asymptotic behavior of
typical orbits can display. For example, we show in any transitive system, the
emprical measures of a typical orbit can cover all emprical measures of dense
orbits and can intersect some physical-like measures. In particular, if the
union set of emprical measures of all dense orbits is not singleton, then the
typical orbit will display historic behavior simultaneously for typical
continuous functions and the limit set of ergodic average along every
continuous function equals to a closed interval composed by the union of limit
sets of ergodic average on all dense orbits. Moreover, if the union set of
emprical measures of all dense orbits contains all ergodic measures, the above
interval equals to the rotation set. These results are not only suitable for
systems with specification-like properties or minimal systems, but also
suitable for many other systems including all general (not assumed uniformly
hyperbolic) nontrivial homoclinic classes and Bowen eyes. Moreover, we
introduce a new property called m-g-product property weaker than classical
specification property and minimal property and nontrivial examples are
constructed.
