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arXiv 2009.065522020-09math.DSmath.RT

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

Siyuan Tang

英文摘要：

We study the cocompact lattices $Γ\subset SO(n,1)$ so that the Laplace-Beltrami operator $Δ$ on $SO(n)\backslash SO(n,1)/Γ$ has eigenvalues in $(0,1/4)$, and then show that there exist time-changes of unipotent flows on $SO(n,1)/Γ$ 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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