Lower Resolvent Bounds and Lyapunov Exponents

被引：2

作者：

Dyatlov, Semyon ^{[1
]}

Waters, Alden ^{[2
]}

机构：

[1] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] UCL, Dept Math, Gower St, London WC1E 6BT, England

来源：

APPLIED MATHEMATICS RESEARCH EXPRESS | 2016年 / Oxford University Press卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.1093/amrx/abv010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a new polynomial lower bound on the scattering resolvent. For that, we construct a quasimode localized on a trajectory. which is trapped in the past, but not in the future. The power in the bound is expressed in terms of the maximal Lyapunov exponent on., and gives the minimal number of derivatives lost in exponential decay of solutions to the wave equation.

引用

页码：68 / 97

页数：30

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