论文标题
Ruelle共振的分析分析性分析的分散性分布
Distribution of Ruelle resonances for real-analytic Anosov diffeomorphisms
论文作者
论文摘要
我们证明了与实用分析的Anosov differemormormings相关的Koopman运算符的Ruelle共振数量的上限：在尺寸$ D $中，大于$ r $的共振数是$ \ MATHCAL {O}（O}（| \ log R |^d）$ r $ n时$ r $ 0 $ 0 $ 0 $。对于在实用分析的歧管上实现Anosov差异的每个连接的组件，我们证明了二分法：我们界限中的指数$ d $从来都不是最佳的，或者在密集的子集上是最佳的。使用Bandtlow，Just和Slipantschuk构建的示例，我们看到我们始终处于后一种情况下，对于$ 2 $维的Torus，实际分析的Anosov diffefuremormormormormormormists的连接组件处于后一种情况。
We prove an upper bound for the number of Ruelle resonances for Koopman operators associated to real-analytic Anosov diffeomorphisms: in dimension $d$, the number of resonances larger than $r$ is a $\mathcal{O}(|\log r|^d)$ when $r$ goes to $0$. For each connected component of the space of real-analytic Anosov diffeomorphisms on a real-analytic manifold, we prove a dichotomy: either the exponent $d$ in our bound is never optimal, or it is optimal on a dense subset. Using examples constructed by Bandtlow, Just and Slipantschuk, we see that we are always in the latter situation for connected components of the space of real-analytic Anosov diffeomorphisms on the $2$-dimensional torus.
