7 citations · 7 across the 6 of their papers we have counts for
7 papers
Singular hyperbolicity of generic three dimensional vector fields
Manseob Lee
In the paper, we show that for a generic vector field on a closed three dimensional manifold , any isolated transitive set of is singular hyperbolic. It is a parti…
Inverse pseudo orbit tracing property for robust diffeomorphisms
Manseob Lee
Let be a closed smooth Riemannian manifold , and let be a diffeomorphism. Herein, we demonstrate that (i) if has the robustly inverse shadowing property…
Kinematic N-expansive flows
Manseob Lee, Jumi Oh, Junmi Park
In light of the rich results of expansiveness in the dynamics of diffeomorphisms, it is natural to consider another notions of expansiveness such as countably-expansive, measure ex…
Continuum-wise expansiveness for generic diffeomorphisms
Manseob Lee
Let be a closed smooth manifold and let be a diffeomorphism. -generically, a continuum-wise expansive satisfies Axiom A without cycles. Moreover, there is a par…
Stable weakly shadowable volume-preserving systems are volume-hyperbolic
Mario Bessa, Manseob Lee, Sandra Vaz
We prove that any C1-stably weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E + F. Moreover, both E and F are volume…
Volume Preserving Diffeomorphisms with Inverse Shadowing
Manseob Lee
Let f be a volume-preserving diffeomorphism of a closed C^\infty n-dimensional Riemannian manifold M: In this paper, we prove the equivalence between the following conditions: (a)…