Loading...
Person
da Costa Cruz de Oliveira Torres, Maria Joana
4 results
Search Results
Now showing 1 - 4 of 4
- Hyperbolicity through stable shadowing for generic geodesic flowsPublication . Bessa, Mário; Dias, João Lopes; Torres, Maria JoanaWe prove that the closure of the closed orbits of a generic geodesic flow on a closed Riemannian n ≥ 2 dimensional manifold is a uniformly hyperbolic set if the shadowing property holds C2-robustly on the metric. We obtain analogous results using weak specification and the shadowing property allowing bounded time reparametrization.
- On the periodic orbits, shadowing and strong transitivity of continuous flowsPublication . Bessa, Mário; Torres, Maria Joana; Varandas, PauloWe prove that chaotic flows (i.e. flows that satisfy the shadowing property and have a dense subset of periodic orbits) satisfy a reparametrized gluing orbit property similar to the one introduced in Bomfim and Varandas (2015). In particular, these are strongly transitive in balls of uniform radius. We also prove that the shadowing property for a flow and a generic time-t map, and having a dense subset of periodic orbits hold for a C0-Baire generic subset of Lipschitz vector fields, that generate continuous flows. Similar results also hold for C0-generic homeomorphisms and, in particular, we deduce that chain recurrent classes of C0-generic homeomorphisms have the gluing orbit property.
- On shadowing and hyperbolicity for geodesic flows on surfacesPublication . Bessa, Mário; Dias, João Lopes; Torres, Maria JoanaWe prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the specification properties. Despite the Hamiltonian nature of the geodesic flow, the arguments in the present paper differ completely from those used in Bessa et al. (2013) for Hamiltonian systems.
- There are no proper topological hyperbolic homoclinic classes for area-preserving mapsPublication . Bessa, Mário; Torres, Maria JoanaWe begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class Λ associated with an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then Λ = M and f is an Anosov homeomorphism.