Extension of invariant manifold theorems to normally hyperbolic compact invariant sets

Let $A^+$ and $A^-$ be general normally hyperbolic compact invariant sets of the respective limit systems. Invariant manifold extension conjecture. The statements for equilibria in the theorems concerning saddle and sink invariant manifolds also hold for $A^+$ and $A^-$. This would extend the paper's results from equilibria to more complicated compact invariant sets, including periodic orbits and tori; the extension to general normally hyperbolic compact invariant sets, especially strange ones, remains open.