  In the previous work, we introduced a method for constructing invariant
probability measures of a large class of non-singular volume-preserving flows
on closed, oriented odd-dimensional smooth manifolds with pseudoholomorphic
curve techniques from symplectic geometry. The technique requires existence of
certain pseudoholomorphic curves satisfying some weak assumptions. In this
work, we appeal to Gromov-Witten theory and Seiberg-Witten theory to construct
large classes of examples where these pseudoholomorphic curves exist. Our
argument uses neck stretching along with new analytical tools from Fish-Hofer's
work on feral pseudoholomorphic curves.
