论文标题
$ \ mathbf {\ textit {u}} $ - 吉布斯的刚度在保守的anosov diffeemorimprips附近，$ \ m athbb {t}^3 $
Rigidity of $\mathbf{\textit{U}}$-Gibbs measures near conservative Anosov diffeomorphisms on $\mathbb{T}^3$
论文作者
论文摘要
我们表明，在$ c^1 $ -neighbourhood $ \ mathcal {u} $中，卷的集合保留了三强$ \ mathbb {t}^3 $，它们在三折rus $ \ mathbb {t}^3 $上具有强烈的部分夸张的中心，任何一部分， $f\in\mathcal{U}\cap\operatorname{Diff}^2(\mathbb{T}^3)$ satisfies the dichotomy: either the strong stable and unstable bundles $E^s$ and $E^u$ of $f$ are jointly integrable, or any fully supported $u$-Gibbs measure of $f$ is SRB.
We show that within a $C^1$-neighbourhood $\mathcal{U}$ 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 unstable bundles $E^s$ and $E^u$ of $f$ are jointly integrable, or any fully supported $u$-Gibbs measure of $f$ is SRB.
