Semi-continuity conjecture for double-rotation attractors

Let $\mathcal{V}$ be the parameter space of finite-type double rotations with a fixed partition, and let the associated map have an attractor. The attractor is semi-continuous with respect to parameters when nearby parameter values produce attractors contained in the appropriate pseudo-Hausdorff neighborhoods. Semi-continuity conjecture. The attractor is semi-continuous with respect to the parameters in $\mathcal{V}$. The claim concerns stability of finite-type attractors under parameter variation and is presented as an expectation based on the preceding discussion; no proof is given in the supplied text.