Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and Exponential Mixing

IF 2.5 1区 数学 Q1 MATHEMATICS
Benjamin Delarue, Daniel Monclair, Andrew Sanders
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引用次数: 0

Abstract

By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique basic hyperbolic set on which the flow is conjugate to the refraction flow of Sambarino. Under the assumption of irreducibility, we utilize the work of Stoyanov to establish spectral estimates for the associated complex Ruelle transfer operators, and by way of corollary: exponential mixing, exponentially decaying error term in the prime orbit theorem, and a spectral gap for the Ruelle zeta function. With no irreducibility assumption, results of Dyatlov-Guillarmou imply the global meromorphic continuation of zeta functions with smooth weights, as well as the existence of a discrete spectrum of Ruelle-Pollicott resonances and (co)-resonant states. We apply our results to space-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds of Danciger-Guéritaud-Kassel, and the Benoist-Hilbert geodesic flow for strictly convex real projective manifolds.

局部齐次公理A流I:投影Anosov子群与指数混合
通过在合适的齐次空间中构造一个非空的不连续域,证明了具有唯一基本双曲集的局部齐次接触公理a动力系统的无扭转投影Anosov子群是其单群,且该系统上的流动共轭于Sambarino折射流。在不可约的假设下,我们利用Stoyanov的工作建立了相关复Ruelle传递算子的谱估计,并通过推论:指数混合、素轨道定理中的指数衰减误差项和Ruelle zeta函数的谱间隙。在没有不可约假设的情况下,Dyatlov-Guillarmou的结果暗示了具有光滑权值的zeta函数的全局亚纯延后,以及Ruelle-Pollicott共振和(co)-共振态的离散谱的存在。我们将我们的结果应用于danciger - gu里多-卡塞尔的凸紧伪黎曼流形的类空间测地线流,以及严格凸实射影流形的Benoist-Hilbert测地线流。
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来源期刊
CiteScore
3.70
自引率
4.50%
发文量
34
审稿时长
6-12 weeks
期刊介绍: Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.
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