Livsic Theorem for Matrix Cocycles Over An Axiom A Flow

被引：0
|
作者：
Lian, Zeng [1 ]
Zhang, Jianhua [1 ]
机构：
[1] Sichuan Univ, Coll Math Sci, Chengdu 610016, Sichuan, Peoples R China
来源：
COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2022年 / 10卷 / 04期
关键词：
Matrix cocycles; Axiom A flow; Lyapunov exponents; COHOMOLOGICAL EQUATION; PERIODIC-ORBITS; STABILITY;
D O I：
10.1007/s40304-021-00250-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove a version of Livsic theorem for a class of matrix cocycles over a C-2 Axiom A flow. As a by-product, an approximative theorem on Lyapunov exponents is also obtained which assets that Lyapunov exponents of a given ergodic measure can be approximated by those of periodic measures.
引用
收藏
页码：681 / 704
页数：24
相关论文
共 50 条
  • [1] Livsic Theorem for matrix cocycles
    Kalinin, Boris
    [J]. ANNALS OF MATHEMATICS, 2011, 173 (02) : 1025 - 1042
  • [2] Livšic Theorem for Matrix Cocycles Over An Axiom A Flow
    Zeng Lian
    Jianhua Zhang
    [J]. Communications in Mathematics and Statistics, 2022, 10 : 681 - 704
  • [3] Livsic theorem for matrix cocycles over nonuniformly hyperbolic systems
    Zou, Rui
    Cao, Yongluo
    [J]. STOCHASTICS AND DYNAMICS, 2019, 19 (02)
  • [4] Livsic theorem for diffeomorphism cocycles
    Avila, Artur
    Kocsard, Alejandro
    Liu, Xiao-Chuan
    [J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2018, 28 (04) : 943 - 964
  • [5] Livsic theorem for low-dimensional diffeomorphism cocycles
    Kocsard, Alejandro
    Potrie, Rafael
    [J]. COMMENTARII MATHEMATICI HELVETICI, 2016, 91 (01) : 39 - 64
  • [6] The Livsic periodic point theorem for non-abelian cocycles
    Parry, W
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1999, 19 : 687 - 701
  • [7] Remarks on Livsic' theory for nonabelian cocycles
    Schmidt, K
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1999, 19 : 703 - 721
  • [8] Livsic theorems for Banach cocycles: Existence and regularity
    Zou, Rui
    Cao, Yongluo
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 280 (05)
  • [9] On a theorem of Livsic
    Aleman, Alexandru
    Martin, R. T. W.
    Ross, William T.
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 264 (04) : 999 - 1048
  • [10] A Livic Theorem for Matrix Cocycles Over Non-uniformly Hyperbolic Systems
    Backes, Lucas
    Poletti, Mauricio
    [J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2019, 31 (04) : 1825 - 1838
12345