### Abstract

We give a proof of cocycle rigidity in Hölder and smooth categories for Cartan actions on SL(n,ℝ)/Γ and SL(n,ℂ)/Γ for n ≥ 3 and Γ cocompact lattice, and for restrictions of those actions to subspaces which contain a two-dimensional plane in general position. This proof does not use harmonic analysis, it relies completely on the structure of stable and unstable foliations of the action. The key new ingredient is the use of the description of generating relations in the group SL_{n}.

Original language | English (US) |
---|---|

Pages (from-to) | 985-1005 |

Number of pages | 21 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 13 |

Issue number | 4 |

State | Published - Nov 1 2005 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

^{k}actions.

*Discrete and Continuous Dynamical Systems*,

*13*(4), 985-1005.

}

^{k}actions',

*Discrete and Continuous Dynamical Systems*, vol. 13, no. 4, pp. 985-1005.

**Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic ℝ ^{k} actions.** / Damjanović, Danijela; Katok, Anatoly.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic ℝk actions

AU - Damjanović, Danijela

AU - Katok, Anatoly

PY - 2005/11/1

Y1 - 2005/11/1

N2 - We give a proof of cocycle rigidity in Hölder and smooth categories for Cartan actions on SL(n,ℝ)/Γ and SL(n,ℂ)/Γ for n ≥ 3 and Γ cocompact lattice, and for restrictions of those actions to subspaces which contain a two-dimensional plane in general position. This proof does not use harmonic analysis, it relies completely on the structure of stable and unstable foliations of the action. The key new ingredient is the use of the description of generating relations in the group SLn.

AB - We give a proof of cocycle rigidity in Hölder and smooth categories for Cartan actions on SL(n,ℝ)/Γ and SL(n,ℂ)/Γ for n ≥ 3 and Γ cocompact lattice, and for restrictions of those actions to subspaces which contain a two-dimensional plane in general position. This proof does not use harmonic analysis, it relies completely on the structure of stable and unstable foliations of the action. The key new ingredient is the use of the description of generating relations in the group SLn.

UR - http://www.scopus.com/inward/record.url?scp=28444485985&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28444485985&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:28444485985

VL - 13

SP - 985

EP - 1005

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 4

ER -

^{k}actions. Discrete and Continuous Dynamical Systems. 2005 Nov 1;13(4):985-1005.