Dynamical Resistance Day

Robust transitivity revisited: non-uniformly expanding bundles
06 de Novembro 11h00min | Raúl Ures (SUSTech, Shenzen, China)

Title: Robust transitivity revisited: non-uniformly expanding bundles (video)

We study the relationship between non-uniformly expanding bundles and robust transitivity. In particular, we show that if f is a partially hyperbolic diffeomorphism with mostly expanding center and its stable foliation is minimal, the stable foliation is C1-robustly minimal. This is a consequence of a more general result where the condition of mostly expansiveness is replaced by a weak form of expansion along the center direction.

Our techniques allow us to present new examples of robustly transi- tive diffeomorphisms. For instance, we show that for a generic volume preserving perturbation of the time-one map of the geodesic flow of a surface with constant negative curvature, either the strong stable or the strong unstable foliation is robustly minimal in its dissipative neighborhood. Other examples are DA diffeomorphisms of the 3-torus with enough center-unstable volume expansion; they also have robustly minimal stable foliation. This talk is based in joint works with Jana R. Hertz and Jiagang Yang, and with Marcelo Viana and Jiagang Yang.