论文标题
均质空间以及几何学和数字理论应用的无义轨道
Nondense orbits on homogeneous spaces and applications to geometry and number theory
论文作者
论文摘要
令$ g $为谎言组，$γ\子集g $一个离散子组，$ x = g/γ$，$ f $ a offine Map从$ x $到本身。我们在$ x $的子曼尼弗德$ z $上提供条件，保证一组点$ x \ in x $，带有$ f $ -trajectores避免$ z $的$ x $是超平面绝对的获胜（该属性意味着完整的Hausdorff尺寸，并且在可计数的交叉点下是稳定的）。对于$ x $的单参数措施，证明了类似的结果。这具有在局部对称空间上构建非凡的测量学的应用，以及在整数点处某些函数值集的非密度。
Let $G$ be a Lie group, $Γ\subset G$ a discrete subgroup, $X=G/Γ$, and $f$ an affine map from $X$ to itself. We give conditions on a submanifold $Z$ of $X$ guaranteeing that the set of points $x\in X$ with $f$-trajectories avoiding $Z$ is hyperplane absolute winning (a property which implies full Hausdorff dimension and is stable under countable intersections). A similar result is proved for one-parameter actions on $X$. This has applications to constructing exceptional geodesics on locally symmetric spaces, and to non-density of the set of values of certain functions at integer points.
