# Robust minimality of strong foliations for DA diffeomorphisms: new examples

Date. September 25, 14h00m (UTC/GMT+1)

Speaker. Jana Rodriguez-Hertz (SUSTech)

Title. Robust minimality of strong foliations for DA diffeomorphisms:  new examples

Abstract.

Let f be a C^2 partially hyperbolic diffeomorphisms of T^3 (not necessarily volume preserving or transitive) isotopic to a linear Anosov diffeomorphism A with eigenvalues k_3<1<k_2<k_1. If the set
\{x: \mid \log \det(Tf\mid_{E^{cu}(f)})\mid \leq \log k_1 \} has zero volume inside any unstable leaf of f, then the stable foliation of f is C^1 robustly minimal, i.e., the stable foliation of any diffeomorphism C^1 sufficiently close to f is minimal. In particular, f itself is robustly transitive.
We build, with this criterion, a new example of a C^1 open set of DA diffeomorphisms, such that the strong stable foliation and the strong unstable foliation of any diffeomorphism in this open set are both minimal. The existence of such an example was unknown in this setting. This is a joint work with  R. Ures and J. Yang.

Online Zoom meeting (Session will open some minutes before 14h00)
https://videoconf-colibri.zoom.us/j/92574158618?pwd=WUFDZC9GQ0xPWEVNRE9DZGVkZFY0dz09

Meeting ID: 925 7415 8618

Start Date
Venue
Online seminar

## Speaker

Jana Rodriguez-Hertz

SUSTech

## Area

Dynamical Systems