Non-recurrence conjecture for the residual intersection of homoclinic classes

Let $X$ be a Venice mask supported on a compact $3$-manifold $M$. Let $H_1$ and $H_2$ be two different homoclinic classes in $M(X)$), let $\Lambda=H_1\cap H_2$, and suppose that the decomposition from the cited theorem is

$$\Lambda=S\cup H\cup R.$$

Here, a point is regular if it is not singular, and a point is non-recurrent if it does not return arbitrarily close to itself under the flow. Non-recurrence conjecture. Every regular point $q\in R$ is non-recurrent. The conjecture concerns the dynamics of the residual part of the intersection of distinct homoclinic classes; the source gives no resolution status.