Positive entropy for topological Anosov flows

Let $M$ be the underlying manifold and let $\mathcal{TA}\mathcal{F}(M)$ denote the class of topological Anosov flows on $M$. Write $h_{\mathrm{top}}(\theta)$ for the topological entropy of a flow $\theta$.

Positive topological entropy. Every topological Anosov flow $\theta\in\mathcal{TA}\mathcal{F}(M)$ has

$$h_{\mathrm{top}}(\theta)>0.$$

Positive entropy expresses persistent dynamical complexity and is expected for hyperbolic systems. The source states this as a conjectural property of topological Anosov flows without supplying a resolution.