Browsing by Author "Torres, Maria Joana"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
- On shadowing and hyperbolicity for geodesic flows on surfacesPublication . Bessa, Mario; 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.
- On the periodic orbits, shadowing and strong transitivity of continuous flowsPublication . Bessa, Mario; 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.
- Sobolev homeomorphisms are dense in volume preserving automorphismsPublication . Azevedo, Assis; Azevedo, Davide; Bessa, Mario; Torres, Maria JoanaIn this paper we prove a weak version of Lusin’s theorem for the space of Sobolev [...]