The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
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近双曲 3 流形的 Ruelle zeta 函数为零
DOI：
10.1007/s00222-022-01108-x
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发表时间：
2022
影响因子：
3.1
通讯作者：
Paternain, Gabriel P.
中科院分区：
文献类型：
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作者：
Cekić, Mihajlo;Delarue, Benjamin;Dyatlov, Semyon;Paternain, Gabriel P.
我们证明了对于具有Betti数的紧致双曲3-流形的一般共形度量扰动，Ruelle Zeta函数在零点处的零零点级等于，而在双曲型情况下它等于。这与二维情况相反，在二维情况下，消失的顺序是拓扑不变量。该证明利用动力学Zeta函数的微局部方法，给出了双曲情形下广义Pollicott-Ruelle共振微分形式在0处的几何描述，并用一阶变分进行摄动.为了证明第一种变分是一般非零的，我们引入了一个新的恒等式，该恒等式与调和1-形式的球丛上的共振和余共振2-形式的乘积的推进有关。
We show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifoldwith Betti number, the order of vanishing of the Ruelle zeta function at zero equals, while in the hyperbolic case it is equal to. This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundlewith harmonic 1-forms on.