论文标题
理性Anosov地图上的共鸣
Resonances for rational Anosov maps on the torus
论文作者
论文摘要
介绍了保留某些Reinhardt域的理性托拉尔·阿诺索夫差异性的共振的完整描述。因此，表明每个同二维的二维Anosov差异形态都包含图形的地图，并具有谐振的序列衰减的指数。这是通过引入一组理性的差异性和计算在适当的各向异性高功能上考虑的各个组成算子的共振的方法来实现的。一类示例足够丰富，还包括具有微不足道共振的非线性Anosov图，或者呈指数衰减，以及有或没有区域保护或反向对称性的谐振。
A complete description of resonances for rational toral Anosov diffeomorphisms preserving certain Reinhardt domains is presented. As a consequence it is shown that every homotopy class of two-dimensional Anosov diffeomorphisms contains maps with the sequence of resonances decaying stretched-exponentially. This is achieved by introducing a certain group of rational toral diffeomorphisms and computing the resonances of the respective composition operator considered on suitable anisotropic spaces of hyperfunctions. The class of examples is sufficiently rich to also include non-linear Anosov maps with trivial resonances, or resonances decaying exponentially, as well as with or without area-preservation or reversing symmetries.
