Secondary invariants and the singularity of the Ruelle zeta-function in the central critical point
Secondary invariants and the singularity of the Ruelle zeta-function in the central critical point
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Ruelle zeta 函数在中心临界点的二次不变量和奇点
DOI：
10.1090/s0273-0979-1995-00570-7
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发表时间：
1995
影响因子：
1.3
通讯作者：
A. Juhl
中科院分区：
文献类型：
--
作者：
A. Juhl
秩为1的偶数维紧致局部对称空间X的球丛S（X）上测地线流的Ruelle zeta函数是复平面上的亚纯函数，它满足一个函数方程，该方程将它在s和-s中的值联系起来。其奇点在中心临界点s = 0的多重性仅取决于流的双曲结构，并且可以通过积分与流不变叶理S（X）正则相关的第二特征类来计算，给出了其表示微分形式。
The Ruelle zeta-function of the geodesic flow on the sphere bundle $S(X)$ of an even-dimensional compact locally symmetric space $X$ of rank $1$ is a meromorphic function in the complex plane that satisfies a functional equation relating its values in $s$ and $-s$. The multiplicity of its singularity in the central critical point $s = 0$ only depends on the hyperbolic structure of the flow and can be calculated by integrating a secondary characteristic class canonically associated to the flow- invariant foliations of $S(X)$ for which a representing differential form is given.