论文标题
$ u $ -gibbs的独特性在$ \ mathbb {t}^4 $上的双曲线偏斜产品
Uniqueness of $u$-Gibbs measures for hyperbolic skew products on $\mathbb{T}^4$
论文作者
论文摘要
我们在$ \ mathbb {t}^4 $上研究了某些类别均匀的双曲线偏度产品的$ U $ -GIBBS度量。这些系统具有强大的不稳定和弱的方向。我们表明，$ c^r $ dense和$ c^2 $ - 在此集合中，每个$ u $ -gibbs度量是SRB，尤其是这样的措施。作为此应用，我们可以获得强烈的不稳定叶面的最低限度。
We study the $u$-Gibbs measures of a certain class of uniformly hyperbolic skew products on $\mathbb{T}^4$. These systems have a strong unstable and a weak unstable directions. We show that $C^r$-dense and $C^2$-open in this set every $u$-Gibbs measure is SRB, in particular, there is only one such measure. As an application of this, we can obtain the minimality of the strong unstable foliation.
