洛伦兹群商上幂偶流的新时变

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2020-09-14 DOI:10.3934/jmd.2022002

Siyuan Tang

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引用次数: 3

摘要

我们研究了共压缩格\ begin｛document｝$\Gamma\子集SO（n，1）$\end｛document｝，使得\ begin{document｝$SO（n）\反斜杠SO（n、1，然后证明了在\ begin｛document｝$SO（n，1）/\ Gamma$\ end｛documents｝上存在与未扰动流不可测量共轭的单势流的时间变化。证明的一个主要成分是互补级数分支的更强版本。将其与拉特纳和弗拉米尼奥的作品相结合——福尼就足以达到我们的目的。

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New time-changes of unipotent flows on quotients of Lorentz groups

We study the cocompact lattices \begin{document}$ \Gamma\subset SO(n, 1) $\end{document} so that the Laplace–Beltrami operator \begin{document}$ \Delta $\end{document} on \begin{document}$ SO(n)\backslash SO(n, 1)/\Gamma $\end{document} has eigenvalues in \begin{document}$ (0, \frac{1}{4}) $\end{document}, and then show that there exist time-changes of unipotent flows on \begin{document}$ SO(n, 1)/\Gamma $\end{document} that are not measurably conjugate to the unperturbed ones. A main ingredient of the proof is a stronger version of the branching of the complementary series. Combining it with a refinement of the works of Ratner and Flaminio–Forni is adequate for our purpose.

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来源期刊

Journal of Modern Dynamics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Modern Dynamics (JMD) is dedicated to publishing research articles in active and promising areas in the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research, including: Number theory Symplectic geometry Differential geometry Rigidity Quantum chaos Teichmüller theory Geometric group theory Harmonic analysis on manifolds. The journal is published by the American Institute of Mathematical Sciences (AIMS) with the support of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University.