I think a little more information would be needed, especially for people like me who are unfamiliar with maya.
-For objects, the vibrate tag will give a similar effect to the wiggle expression in After effects.
-For particles, both thinking and generated from a emitter you can create a turbulence field.
-The closest thing to creating something similar to turbulance displace that I can think of I would have to create using expresso and either sub-polygon displacement, and or some other deformer object.
Again, please clarify what effect you are looking for.