Loading...
2 results
Search Results
Now showing 1 - 2 of 2
- Shadowing, expansiveness and specification for C1-conservative systemsPublication . Bessa, Mário; Lee, Manseob; Wen, XiaoWe prove that a C -generic volume-preserving dynamical system (diffeomor- phism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [10, 27], we prove that the C -robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system (diffeomorphism or flow) is Anosov.
- A note on expansiveness and hyperbolicity for generic geodesic flowsPublication . Bessa, MárioIn this short note we contribute to the generic dynamics of geodesic flows associated to metrics on compact Riemannian manifolds of dimension ≥ 2. We prove that there exists a C2-residual subset R of metrics on a given compact Riemannian manifold such that if g∈R, then its associated geodesic flow φ_g(t) is expansive if and only if the closure of the set of periodic orbits of φgt is a uniformly hyperbolic set. For surfaces, we obtain a stronger statement: there exists a C2-residual R such that if g ∈ R, then its associated geodesic flow φgt is expansive if and only if φ_g(t) is an Anosov flow.