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We prove that every singular hyperbolic chain transitive set with asingularity does not admit the shadowing property. Using this result we showthat if a star flow has the shadowing property on its chain recurrent set thenit satisfies Axiom A and the no-cycle conditions; and that if a multisingularhyperbolic set has the shadowing property then it is hyperbolic.

No-shadowing for singular hyperbolic sets with a singularity