Hydraulic oil leaking from air filter housing

So I quit drinking for the past three days to be sure I am seeing what I see. Yep, I have clean hydraulic oil leaking from the air filter housing on my Hitachi UHO83.

The machine smokes a little more than it should on startup but then clears up. When I shut down, hydraulic oil starts dripping in a pretty good stream and will run about a quart on the ground then in a few hours it stops. I don't get it! How is this happening? Turbos?

Hydraulic oil leaking from air filter housing