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arXiv · 2003.05165

No-shadowing for singular hyperbolic sets with a singularity

Xiao Wen·Lan Wen
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Abstract

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

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Xiao Wen, Lan Wen. 2020-03-11. No-shadowing for singular hyperbolic sets with a singularity. https://arxiv.org/abs/2003.05165

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