1 citations · 2 across the 4 of their papers we have counts for
4 papers · 1 filter
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…
A rescaled expansiveness for flows
Xiao Wen, Lan Wen
We introduce a new version of expansiveness for flows. Let be a compact Riemannian manifold without boundary and be a vector field on that generates a flow …
Codimension one structurally stable chain classes
Xiao Wen, Lan Wen
The well known stability conjecture of Palis and Smale states that if a diffeomorphism is structurally stable then the chain recurrent set is hyperbolic. It is natural to ask if th…
On the singular hyperbolicity of star flows
Yi Shi, Shaobo Gan, Lan Wen
We prove for a generic star vector field that, if for every chain recurrent class of all singularities in have the same index, then the chain recurrent set of i…