Gradient flows with wildly embedded closures of separatrices

We show that for any $n\ge4$ there exists an $n$-dimensional closed manifold $M^n$ on which one can define a Morse–Smale gradient flow $f^t$ with two nodes and two saddles such that the closure of the separatrix of some saddle of $f^t$ is a wildly embedded sphere of codimension 2. We also prove that the closures of separatrices of a flow with three equilibrium points are always embedded in a locally flat way.