论文标题
Selberg Zeta功能，尖端加速度以及严格转移操作员方法的存在
Selberg zeta functions, cuspidal accelerations, and existence of strict transfer operator approaches
论文作者
论文摘要
对于几何有限的非压缩的可开发双曲线轨道（包括无限体积的轨道），我们提供了转移操作员家族，其弗雷德尔姆决定因素与Selberg Zeta功能相同。我们的证明产生算法和均匀的结构。该结构是通过外部提供的横截面来启动的，用于在考虑的轨道表面上的地球流量，产生了高度忠实但不均匀扩展的离散动力学系统，对大地测量流进行建模。通过许多算法的减少，扩展，翻译，归纳和加速的步骤，我们将此横截面变成一种仍然非常忠实但现在均匀扩展离散动力系统的横截面。出现的转移操作员家族是在合适的Banach空间上零命令的核。此外，可以包括具有非扩展尖尖的有限维曲折。
For geometrically finite non-compact developable hyperbolic orbisurfaces (including those of infinite volume), we provide transfer operator families whose Fredholm determinants are identical to the Selberg zeta function. Our proof yields an algorithmic and uniform construction. This construction is initiated with an externally provided cross section for the geodesic flow on the considered orbisurface that yields a highly faithful, but non-uniformly expanding discrete dynamical system modelling the geodesic flow. Through a number of algorithmic steps of reduction, extension, translation, induction and acceleration, we turn this cross section into one that yields a still highly faithful, but now uniformly expanding discrete dynamical system. The arising transfer operator family is nuclear of order zero on suitable Banach spaces. In addition, finite-dimensional twists with non-expanding cusp monodromy can be included.
