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In this work we study the existence of singular flows satisfyingshadowing-like properties. More precisely, we prove that if C1 -vector field ona closed manifold induces a chain-recurrent flow containing an attachedhyperbolic singularity of stable or unstable index-one, then this flow cannotsatisfy the shadowing property. If the manifold is non-compact, the vectorfield is complete and non-wandering, we prove that we prove that the existenceof index-one hyperbolic singularities prevents the induced flow to satisfy therescaled-shadowing property introduced in [6].

On the Shadowableness of Flows With Hyperbolic Singularities