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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…
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…
Shadowing, expansiveness and specification for C1-conservative systems
M. Bessa, M. Lee, X. Wen
We prove that a C1-generic volume-preserving dynamical system (diffeomorphism or flow) has the shadowing property or is expansive or has the weak specification property if and only…
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)…
Volume Preserving Diffeomorphisms with Weak and Limit Weak Shadowing
Manseob Lee
Let f be a volume-preserving diffeomorphism of a closed C1 n-dimensional Riemannian manifold M: In this paper, we prove the equivalence between the following conditions: (a) f belo…