Systematic aspect has to do with the way the speaker/writer is viewing
the action when speaking or writing. He can be focusing on the
beginning of the action: "God said, 'Let there be light', and there WAS
(=began to be) light." He can be focusing on the action as a complete
event, with a beginning, a middle and an end: "Yesterday I SPOKE with
Peter." Or he can be focusing on the event as a on-going action:
"While I was speaking to him . . ." This kind of aspect is systematic
in that it is often expressed morphologically ELUON, ELUSA, etc., and
can be attached to any verb. They have names like Perfective,
Imperfective, etc. Aktionsart, in my view, belongs to individual verbs
and forms categories such as "punctual", "durative", etc. Certain kinds
of actions lend themselves to durativeness: eat, sleep, live, study,
know, walk, etc. Others cannot be durative because as actions or events
they are not susceptible to being prolonged: die, arrive, hit, kick,
cough, slap, find, etc. I can't go into great detail here, but the
different kinds of Aktionsart interact different ways with systematic
aspect. For instance, a verb with punctual Aktionsart ('slap') with
perfective aspect typically refers to a single slap: 'Fred slapped
Smitty'. But combined with imperfect aspect tends to express
reiteration: 'Fred was slapping Smitty' (= repeatedly). However, if we
combine a verb with durative Aktionsart with the imperfective, the
result is not necessarily reiterative: "Fred was eating" (no =
repeatedly). It is much more complex than this, but this at least
explains what I'm talking about. There are good books devoted to aspect
such as one titled, curiously, "Aspect" by Bernard Comrie (Cambridge
University Press). And of course there's Stanley Porter's book on Greek
aspect (which I don't have because I couldn't afford it!).
Cheers,
Ron Ross