Non-shadowing conjecture for chain-recurrent sets with attached singularities

Let $M$ be a closed manifold and let $X$ be a $C^1$ vector field on $M$. Let $\Lambda\subset M$ be a chain-recurrent set with an attached singularity. Attached-singularity non-shadowing conjecture. Then $\Lambda$ does not have the shadowing property. The conjecture proposes that the presence of any attached singularity is sufficient to prevent shadowing for a chain-recurrent set. The paper proves non-shadowing in some cases, but the general assertion is presented as an open question.