Open-and-dense sink/source conjecture for flows and semiflows

Let $M$ range over manifolds, and consider continuous flows or smooth semiflows on $M$. An extended notion of sectional asymptotic expansion or contraction along trajectories is assumed to be available.

Open-and-dense sink/source conjecture. There exists an open and dense family of continuous flows or smooth semiflows on manifolds for which sectional asymptotic expansion or contraction along trajectories ensures the existence of sources or sinks.

The conjecture seeks analogues of the paper's sink and source results beyond vector fields, but the required extended notion and the precise topology are not specified in the supplied text.