论文标题
某些对角线流量的加权不良的复合载体和有界轨道
Weighted badly approximable complex vectors and bounded orbits of certain diagonalizable flows
论文作者
论文摘要
我们显示了An，Ghosh，Guan和Ly的定理的类似物，并在加权较差的矢量中显示了完全虚构的数字字段。 We show that for $G=\mathrm{SL}_2(\mathbb{C})\times\dots\times\mathrm{SL}_2(\mathbb{C})$ and $Γ<G$ a lattice subgroup, the points of $G/Γ$ with bounded orbits under a one-parameter Ad-semisimple subgroup of $G$形成超平面吸毒式套装。作为应用程序，我们还提供了Esdahl-Schou和Kristensen的结果的概括，内容涉及一组差不多的复数。
We show an analogue of a theorem of An, Ghosh, Guan, and Ly on weighted badly approximable vectors for totally imaginary number fields. We show that for $G=\mathrm{SL}_2(\mathbb{C})\times\dots\times\mathrm{SL}_2(\mathbb{C})$ and $Γ<G$ a lattice subgroup, the points of $G/Γ$ with bounded orbits under a one-parameter Ad-semisimple subgroup of $G$ form a hyperplane-absolute-winning set. As an application, we also provide a generalization of a result of Esdahl-Schou and Kristensen about the set of badly approximable complex numbers.
