LOCAL RIGIDITY OF CERTAIN SOLVABLE GROUP ACTIONS ON TORI

被引：2
|
作者：
Liu, Qiao [1 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2021年 / 41卷 / 02期
关键词：
local rigidity; group action; Anosov diffeomorphism; CONJUGACY;
D O I：
10.3934/dcds.2020269
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a local rigidity property of Z proportional to(lambda) R affine action on tori generated by an irreducible toral automorphism and a linear flow along an eigenspace. Such an action exhibits a weak version of local rigidity, i.e., any smooth perturbations close enough to an affine action is smoothly conjugate to the affine action up to constant time change.
引用
收藏
页码：553 / 567
页数：15
相关论文
共 50 条
  • [1] Rigidity of certain solvable actions on the sphere
    Asaoka, Masayuki
    GEOMETRY & TOPOLOGY, 2012, 16 (03) : 1835 - 1857
  • [2] Rigidity of group actions on solvable Lie groups
    Burkhard Wilking
    Mathematische Annalen, 2000, 317 : 195 - 237
  • [3] LOCAL RIGIDITY OF CERTAIN ACTIONS OF SOLVABLE GROUPS ON THE BOUNDARIES OF RANK-ONE SYMMETRIC SPACES
    Okada, Mao
    JOURNAL OF MODERN DYNAMICS, 2021, 17 : 111 - 143
  • [4] Global rigidity of solvable group actions on S1
    Burslem, L
    Wilkinson, A
    GEOMETRY & TOPOLOGY, 2004, 8 : 877 - 924
  • [5] GLOBAL RIGIDITY OF HIGHER RANK ANOSOV ACTIONS ON TORI AND NILMANIFOLDS
    Fisher, David
    Kalinin, Boris
    Spatzier, Ralf
    Davis, James F.
    JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 26 (01) : 167 - 198
  • [6] RIGIDITY OF RANDOM GROUP ACTIONS
    Jung, Woochul
    Lee, Keonhee
    Morales, Carlos
    Oh, Jumi
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (12) : 6845 - 6854
  • [7] LOCAL RIGIDITY OF PARTIALLY HYPERBOLIC ACTIONS
    Wang, Zhenqi Jenny
    ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES, 2010, 17 : 68 - 79
  • [8] Local Rigidity of Diophantine Translations in Higher-dimensional Tori
    Karaliolios, Nikolaos
    REGULAR & CHAOTIC DYNAMICS, 2018, 23 (01): : 12 - 25
  • [9] Local Rigidity of Diophantine Translations in Higher-dimensional Tori
    Nikolaos Karaliolios
    Regular and Chaotic Dynamics, 2018, 23 : 12 - 25
  • [10] Non-rigidity of partially hyperbolic abelian C1 -actions on tori
    Hertz, Federico Rodriguez
    Wang, Zhiren
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2025, 45 (02) : 573 - 594
12345