July  2008, 2(3): 509-540. doi: 10.3934/jmd.2008.2.509

Regularity of conjugacies of algebraic actions of Zariski-dense groups

1. 

School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom

2. 

Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506, United States

3. 

Department of Mathematics, 2074 East Hall, 530 Church Street, University of Michigan, Ann Arbor, MI 48109-1043, United States

Received  April 2008 Published  April 2008

Let $\alpha_0$ be an affine action of a discrete group $\Gamma$ on a compact homogeneous space $X$ and $\alpha_1$ a smooth action of $\Gamma$ on $X$ which is $C^1$-close to $\alpha_0$. We show that under some conditions, every topological conjugacy between $\alpha_0$ and $\alpha_1$ is smooth. In particular, our results apply to Zariski-dense subgroups of $SL_d(\mathbb{Z})$ acting on the torus $\mathbb{T}^d$ and Zariski-dense subgroups of a simple noncompact Lie group $G$ acting on a compact homogeneous space $X$ of $G$ with an invariant measure.
Citation: Alexander Gorodnik, Theron Hitchman, Ralf Spatzier. Regularity of conjugacies of algebraic actions of Zariski-dense groups. Journal of Modern Dynamics, 2008, 2 (3) : 509-540. doi: 10.3934/jmd.2008.2.509
[1]

Qiao Liu. Local rigidity of certain solvable group actions on tori. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 553-567. doi: 10.3934/dcds.2020269

[2]

Laurent Di Menza, Virginie Joanne-Fabre. An age group model for the study of a population of trees. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020464

[3]

Kien Trung Nguyen, Vo Nguyen Minh Hieu, Van Huy Pham. Inverse group 1-median problem on trees. Journal of Industrial & Management Optimization, 2021, 17 (1) : 221-232. doi: 10.3934/jimo.2019108

2019 Impact Factor: 0.465

Metrics

  • PDF downloads (22)
  • HTML views (0)
  • Cited by (0)

[Back to Top]