The topological volume-preservation problem for Anosov flows

Let $\Phi$ be an Anosov flow. It is topologically equivalent to a volume-preserving flow when it is topologically equivalent to an Anosov flow that preserves a volume. Volume-preservation problem. Any topologically transitive Anosov flow is topologically equivalent to a volume-preserving one. The paper poses this as a question for higher codimension after proving the codimension-one case; it does not report a general resolution or counterexample.