论文标题
Ruelle-Taylor的共鸣Anosov Actions
Ruelle-Taylor resonances of Anosov actions
论文作者
论文摘要
通过J. Taylor开发的微局部方法和一个共同体理论，我们为$ \ Mathbb {r}^κ$ -Anosov行动定义了关节ruelle共振谱的概念。我们证明，这些ruelle-taylor共振符合弗雷德姆理论，是固有的，形成了$ \ mathbb {c}^κ$的离散子集，其中$λ= 0 $始终是领先的共鸣。 $ 0 $的联合共振状态产生了SRB类型的一些新度量，这些措施的混合特性与纯粹虚构共振的存在有关。本文开发的光谱理论特别适用于Weyl室流的情况，并提供了一种研究此类流的新方法。
Combining microlocal methods and a cohomological theory developped by J. Taylor, we define for $\mathbb{R}^κ$-Anosov actions a notion of joint Ruelle resonance spectrum. We prove that these Ruelle-Taylor resonances fit into a Fredholm theory, are intrinsic and form a discrete subset of $\mathbb{C}^κ$, with $λ=0$ being always a leading resonance. The joint resonant states at $0$ give rise to some new measures of SRB type and the mixing properties of these measures are related to the existence of purely imaginary resonances. The spectral theory developed in this article applies in particular to the case of Weyl chamber flows and provides a new way to study such flows.
