Pollicott-Ruelle Resonances for Open Systems

被引：48

作者：

Dyatlov, Semyon ^{[1
]}

Guillarmou, Colin ^{[2
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Ecole Normale Super, CNRS, UMR 8553, DMA, 45 Rue Ulm, F-75230 Paris 05, France

来源：

ANNALES HENRI POINCARE | 2016年 / 17卷 / 11期

关键词：

CONTACT ANOSOV-FLOWS; AXIOM-A FLOWS; ZETA-FUNCTIONS; FREDHOLM DETERMINANTS; HYPERBOLIC DIFFEOMORPHISMS; NEGATIVE CURVATURE; DYNAMICAL-SYSTEMS; EXPANDING MAPS; SPECTRUM; SPACES;

D O I：

10.1007/s00023-016-0491-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We define Pollicott-Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A flows. These resonances are the poles of the meromorphic continuation of the resolvent of the generator of the flow and they describe decay of classical correlations. As an application, we show that the Ruelle zeta function extends meromorphically to the entire complex plane.

引用

页码：3089 / 3146

页数：58

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