Exponential mixing of frame flows for convex cocompact hyperbolic manifolds

被引：5

作者：

Sarkar, Pratyush ^{[1
]}

Winter, Dale ^{[1
]}

机构：

[1] Yale Univ, Dept Math, New Haven, CT 06511 USA

来源：

COMPOSITIO MATHEMATICA | 2021年 / 157卷 / 12期

关键词：

convex cocompact subgroup; Zariski dense subgroup; hyperbolic manifold; frame flow; mixing; exponential mixing; transfer operator; Dolgopyat operator; asymptotic formula; matrix coefficient; equidistribution; holonomy; Bowen-Margulis-Sullivan measure; RUELLE TRANSFER OPERATORS; INVARIANT-MEASURES; EQUIDISTRIBUTION; AXIOM; POINTS; HOLONOMIES; ORBITS; SETS;

D O I：

10.1112/S0010437X21007600

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen-Margulis-Sullivan measure. Some immediate applications include an asymptotic formula for matrix coefficients with an exponential error term as well as the exponential equidistribution of holonomy of closed geodesics. The main technical result is a spectral bound on transfer operators twisted by holonomy, which we obtain by building on Dolgopyat's method.

引用

页码：2585 / 2634

页数：51

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