Abstract

We show that within a C^{1} -neighborhood {\mathcal{U}} of the set of volume preserving Anosov diffeomorphisms on the three-torus {\mathbb{T}^3} which are strongly partially hyperbolic with expanding center, any f\in{\mathcal{U}}\cap{\operatorname{Diff}^2(\mathbb{T}^3)} satisfies the dichotomy: either the strong-stable and strong-unstable bundles E^{s} , E^{u} of f are jointly integrable, or any fully supported u -Gibbs measure of f is SRB.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.