  In this work we study the existence of singular flows satisfying
shadowing-like properties. More precisely, we prove that if C1 -vector field on
a closed manifold induces a chain-recurrent flow containing an attached
hyperbolic singularity of stable or unstable index-one, then this flow cannot
satisfy the shadowing property. If the manifold is non-compact, the vector
field is complete and non-wandering, we prove that we prove that the existence
of index-one hyperbolic singularities prevents the induced flow to satisfy the
rescaled-shadowing property introduced in [6].
