Open AccessNew time-changes of unipotent flows on quotients of Lorentz groups
Author(s) -
Siyuan Tang
Publication year - 2022
Publication title -
journal of modern dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.668
H-Index - 25
eISSN - 1930-532X
pISSN - 1930-5311
DOI - 10.3934/jmd.2022002
Subject(s) - mathematics , combinatorics , unipotent , quotient , arithmetic , algebra over a field , discrete mathematics , pure mathematics
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.