非对易toral自同态的同时稠密轨道和非稠密轨道
Simultaneous dense and nondense orbits for noncommuting toral endomorphisms
摘要：
设$S$和$T$是$\mathbb{T}^d$的双曲自同态，且$S$收缩的子空间与$T$收缩的子空间的跨度为$\mathbb{R}^d$ .证明了在$S$下具有等分布轨道的点集与在$T$下具有非稠密轨道的点集的交的豪斯多夫维数是满的.在$S$和$T$是拟双曲自同构的情况下，我们证明了当我们假设$\mathbb{R}^d$被由$S$和$T$收缩的子空间以及$S$和$T$的中心特征空间所张成时，交集的豪斯多夫维数又是满的.
英文摘要：
Let $S$ and $T$ be hyperbolic endomorphisms of $\mathbb{T}^d$ with the property that the span of the subspace contracted by $S$ along with the subspace contracted by $T$ is $\mathbb{R}^d$. We show that the Hausdorff dimension of the intersection of the set of points with equidistributing orbits under $S$ with the set of points with nondense orbit under $T$ is full. In the case that $S$ and $T$ are quasihyperbolic automorphisms, we prove that the Hausdorff dimension of the intersection is again full when we assume that $\mathbb{R}^d$ is spanned by the subspaces contracted by $S$ and $T$ along with the central eigenspaces of $S$ and $T$.
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