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On \begin{document}$ \epsilon $\end{document}-escaping trajectories in homogeneous spaces
Discrete and Continuous Dynamical Systems ( IF 1.1 ) Pub Date : 2020-10-30 , DOI: 10.3934/dcds.2020365 Federico Rodriguez Hertz , , Zhiren Wang
Discrete and Continuous Dynamical Systems ( IF 1.1 ) Pub Date : 2020-10-30 , DOI: 10.3934/dcds.2020365 Federico Rodriguez Hertz , , Zhiren Wang
Let $ G/\Gamma $ be a finite volume homogeneous space of a semisimple Lie group $ G $, and $ \{\exp(tD)\} $ be a one-parameter $ \operatorname{Ad} $-diagonalizable subgroup inside a simple Lie subgroup $ G_0 $ of $ G $. Denote by $ Z_{\epsilon,D} $ the set of points $ x\in G/\Gamma $ whose $ \{\exp(tD)\} $-trajectory has an escape for at least an $ \epsilon $-portion of mass along some subsequence. We prove that the Hausdorff codimension of $ Z_{\epsilon,D} $ is at least $ c\epsilon $, where $ c $ depends only on $ G $, $ G_0 $ and $ \Gamma $.
中文翻译:
上\ begin {document} $ \ epsilon $ \ end {document} 均匀空间中的逃逸轨迹
令$ G / \ Gamma $为半简单李群$ G $的有限体积齐次空间,而$ \ {\ exp(tD)\} $为单参数$ \ operatorname {Ad} $-对角线化子组$ G $的简单Lie子组$ G_0 $。用$ Z _ {\ epsilon,D} $表示点集$ x \ in G / \ Gamma $,其中$ \ {\ exp(tD)\} $轨迹至少有$ \ epsilon $-一些子序列的质量部分。我们证明$ Z _ {\ epsilon,D} $的Hausdorff余维至少为$ c \ epsilon $,其中$ c $仅取决于$ G $,$ G_0 $和$ \ Gamma $。
更新日期:2020-11-16
中文翻译:
上
令$ G / \ Gamma $为半简单李群$ G $的有限体积齐次空间,而$ \ {\ exp(tD)\} $为单参数$ \ operatorname {Ad} $-对角线化子组$ G $的简单Lie子组$ G_0 $。用$ Z _ {\ epsilon,D} $表示点集$ x \ in G / \ Gamma $,其中$ \ {\ exp(tD)\} $轨迹至少有$ \ epsilon $-一些子序列的质量部分。我们证明$ Z _ {\ epsilon,D} $的Hausdorff余维至少为$ c \ epsilon $,其中$ c $仅取决于$ G $,$ G_0 $和$ \ Gamma $。