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math.DS2020★ 1 cited
No-shadowing for singular hyperbolic sets with a singularity
Xiao Wen, Lan Wen
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 shadowi…
math.DS2020
On the partial hyperbolicity of robustly transitive sets with singularities
Xiao Wen, Dawei Yang
Homoclinic tangencies and singular hyperbolicity are involved in the Palis conjecture for vector fields. Typical three dimensional vector fields are well understood by recent works…