Livsic theorems and stable ergodicity for group extensions of hyperbolic systems with discontinuities

被引：6
|
作者：
Nicol, M [1 ]
Scott, A [1 ]
机构：
[1] Univ Surrey, Dept Math & Stat, Guildford GU2 7XH, Surrey, England
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2003年 / 23卷
关键词：
D O I：
10.1017/S014338570300021X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove measurable Livsic theorems for Lie group valued cocycles over certain classes of uniformly hyperbolic maps with discontinuities, in particular the beta-transformation, C-2 Markov maps and a simple class of total linked twist maps. As an application, we establish stable ergodicity results for compact group extensions of certain classes of uniformly hyperbolic systems with discontinuities.
引用
收藏
页码：1867 / 1889
页数：23
相关论文
共 50 条
  • [1] LIVSIC THEORY FOR COMPACT GROUP EXTENSIONS OF HYPERBOLIC SYSTEMS
    Dolgopyat, Dmitry
    [J]. MOSCOW MATHEMATICAL JOURNAL, 2005, 5 (01) : 55 - U6667
  • [2] The Livsic cocycle equation for compact Lie group extensions of hyperbolic systems
    Parry, W
    Pollicott, M
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1997, 56 : 405 - 416
  • [3] Livsic theorems for hyperbolic flows
    Walkden, CP
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (03) : 1299 - 1313
  • [4] Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets
    Field, M
    Melbourne, I
    Török, A
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 : 517 - 551
  • [5] Stable transitivity of Heisenberg group extensions of hyperbolic systems
    Nitica, Viorel
    Toeroek, Andrei
    [J]. NONLINEARITY, 2014, 27 (04) : 661 - 683
  • [6] Livsic regularity theorems for twisted cocycle equations over hyperbolic systems
    Walkden, CP
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2000, 61 : 286 - 300
  • [7] Livsic theorems, maximizing measures and the stable norm
    Pollicott, M
    Sharp, R
    [J]. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2004, 19 (01): : 75 - 88
  • [8] Transitivity of Heisenberg group extensions of hyperbolic systems
    Melbourne, Ian
    Nitica, Viorel
    Toeroek, Andrei
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2012, 32 : 223 - 235
  • [9] Stable Transitivity of Certain Noncompact Extensions of Hyperbolic Systems
    Ian Melbourne
    Viorel Niţică
    Andrei Török
    [J]. Annales Henri Poincaré, 2005, 6 : 725 - 746
  • [10] Stable transitivity of certain noncompact extensions of hyperbolic systems
    Melbourne, I
    Nitica, V
    Török, A
    [J]. ANNALES HENRI POINCARE, 2005, 6 (04): : 725 - 746
12345