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- On C1-robust transitivity of volume-preserving flowsPublication . Bessa, Mário; Rocha, JorgeWe prove that a divergence-free and C1-robustly transitive vector field has no singularities. Moreover, if the vector field is smooth enough then the linear Poincaré flow associated to it admits a dominated splitting over M.
- Denseness of ergodicity for a class of volume-preserving flowsPublication . Bessa, Mário; Rocha, JorgeWe consider the class of C1 partially hyperbolic volume-preserving flows with one-dimensional central direction endowed with the C 1 -Whitney topology. We prove that, within this class, any flow can be approximated by an ergodic C2 volume-preserving flow and so, as a consequence, ergodicity is dense.
- Three-dimensional conservative star flows are AnosovPublication . Bessa, Mário; Rocha, JorgeA divergence-free vector field satisfies the star property if any divergence-free vector field in some C1-neighborhood has all the singularities and all closed orbits hyperbolic. In this article we prove that any divergence- free star vector field defined in a closed three-dimensional manifold is Anosov. Moreover, we prove that a C1-structurally stable three-dimensional conserva- tive flow is Anosov.
- Hyperbolicity and stability for Hamiltonian flowsPublication . Bessa, Mário; Rocha, Jorge; Torres, Maria JoanaWe prove that a Hamiltonian star system, defined on a 2d-dimen- sional symplectic manifold M (d 2), is Anosov. As a consequence we obtain the proof of the stability conjecture for Hamiltonians. This generalizes the 4-dimensional results in Bessa et al. (2010) [5].