American Institute of Mathematical Sciences

Advanced
May  2010, 27(2): 609-615. doi: 10.3934/dcds.2010.27.609

Rigidity of real-analytic actions of $SL(n,\Z)$ on $\T^n$: A case of realization of Zimmer program

Anatole Katok 1, and  Federico Rodriguez Hertz 2,

1. 

Department of Mathematics, Penn State University, University Park, State College, PA 16802
2. 

IMERL-Facultad de Ingeniería, Universidad de la República, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay

Received  February 2010 Published  February 2010

We prove that any real-analytic action of $SL(n,\Z),n\ge 3$ with standard homotopy data that preserves an ergodic measure $\mu$ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard linear action on the complement to a finite union of periodic orbits.
Keywords: Global rigidity, Zimmer program., real analytic.
Mathematics Subject Classification: Primary: 37C15; Secondary: 37C85, 22F0.
Citation: Anatole Katok, Federico Rodriguez Hertz. Rigidity of real-analytic actions of $SL(n,\Z)$ on $\T^n$: A case of realization of Zimmer program. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 609-615. doi: 10.3934/dcds.2010.27.609
[1]

Xuanji Hou, Lei Jiao. On local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3125-3152. doi: 10.3934/dcds.2016.36.3125
[2]

Xuanji Hou, Jiangong You. Local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 441-454. doi: 10.3934/dcds.2009.24.441
[3]

I. Baldomá, Àlex Haro. One dimensional invariant manifolds of Gevrey type in real-analytic maps. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 295-322. doi: 10.3934/dcdsb.2008.10.295
[4]

Federico Rodriguez Hertz. Global rigidity of certain Abelian actions by toral automorphisms. Journal of Modern Dynamics, 2007, 1 (3) : 425-442. doi: 10.3934/jmd.2007.1.425
[5]

Dehua Wang. Global solution for the mixture of real compressible reacting flows in combustion. Communications on Pure & Applied Analysis, 2004, 3 (4) : 775-790. doi: 10.3934/cpaa.2004.3.775
[6]

Uchida Hidetake. Analytic smoothing effect and global existence of small solutions for the elliptic-hyperbolic Davey-Stewartson system. Conference Publications, 2001, 2001 (Special) : 182-190. doi: 10.3934/proc.2001.2001.182
[7]

Marcel Braukhoff. Global analytic solutions of the semiconductor Boltzmann-Dirac-Benney equation with relaxation time approximation. Kinetic & Related Models, 2020, 13 (1) : 187-210. doi: 10.3934/krm.2020007
[8]

Xiantao Xiao, Jian Gu, Liwei Zhang, Shaowu Zhang. A sequential convex program method to DC program with joint chance constraints. Journal of Industrial & Management Optimization, 2012, 8 (3) : 733-747. doi: 10.3934/jimo.2012.8.733
[9]

Anas Eskif, Julio C. Rebelo. Global rigidity of conjugations for locally non-discrete subgroups of $ {\rm {Diff}}^{\omega} (S^1) $. Journal of Modern Dynamics, 2019, 15: 41-93. doi: 10.3934/jmd.2019013
[10]

Ted Greenwood. Superstar of the Sloan Minority Ph.D. Program. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1539-1540. doi: 10.3934/mbe.2013.10.1539
[11]

Xin Zhao, Jinyan Fan. On subspace properties of the quadratically constrained quadratic program. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1625-1640. doi: 10.3934/jimo.2017010
[12]

James H. Elder. A new training program in data analytics & visualization. Big Data & Information Analytics, 2016, 1 (1) : i-iii. doi: 10.3934/bdia.2016.1.1i
[13]

Jaume Llibre, Claudia Valls. On the analytic integrability of the Liénard analytic differential systems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 557-573. doi: 10.3934/dcdsb.2016.21.557
[14]

A. Kononenko. Twisted cocycles and rigidity problems. Electronic Research Announcements, 1995, 1: 26-34.

[15]

Jean Dolbeault, Maria J. Esteban, Gaspard Jankowiak. Onofri inequalities and rigidity results. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3059-3078. doi: 10.3934/dcds.2017131
[16]

Ilesanmi Adeboye, Harrison Bray, David Constantine. Entropy rigidity and Hilbert volume. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1731-1744. doi: 10.3934/dcds.2019075
[17]

Mads R. Bisgaard. Mather theory and symplectic rigidity. Journal of Modern Dynamics, 2019, 15: 165-207. doi: 10.3934/jmd.2019018
[18]

Woochul Jung, Keonhee Lee, Carlos Morales, Jumi Oh. Rigidity of random group actions. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 0-0. doi: 10.3934/dcds.2020130
[19]

David W. Pravica, Michael J. Spurr. Analytic continuation into the future. Conference Publications, 2003, 2003 (Special) : 709-716. doi: 10.3934/proc.2003.2003.709
[20]

Peter K. Friz, I. Kukavica, James C. Robinson. Nodal parametrisation of analytic attractors. Discrete & Continuous Dynamical Systems - A, 2001, 7 (3) : 643-657. doi: 10.3934/dcds.2001.7.643

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (33)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences