论文标题
局部恒定的旋转和应用的均匀准多层性
Uniform quasi-multiplicativity of locally constant cocycles and applications
论文作者
论文摘要
在本文中，我们表明，在不可约性假设下，本地恒定的共生$ \ Mathcal {a} $是$ k $ quasi乘法。更准确地说，我们表明，如果$ \ nathcal {a}^t $和$ \ nathcal {a}^{\ wedge m} $对于每个$ t \ t \ id d $ d $和$ 1 \ leq m \ leq m \ leq m \ leq d-1 $都是不可记论的，那么\ Mathbb {n} $，这意味着$ \ Mathcal {a} $是$ k $ -quasi乘法。我们应用结果表明，唯一的亚基平衡吉布斯状态为$ψ$ - 混合并计算圆柱缩小目标和复发集的Hausdorff维度。
In this paper, we show that a locally constant cocycle $\mathcal{A}$ is $k$-quasi multiplicative under the irreducibility assumption. More precisely, we show that if $\mathcal{A}^t$ and $\mathcal{A}^{\wedge m}$ are irreducible for every $t \mid d$ and $1\leq m \leq d-1$, then $\mathcal{A}$ is $k$-uniformly spannable for some $k\in \mathbb{N}$, which implies that $\mathcal{A}$ is $k$-quasi multiplicative. We apply our results to show that the unique subadditive equilibrium Gibbs state is $ψ$-mixing and calculate the Hausdorff dimension of cylindrical shrinking target and recurrence sets.
