GAFA Geometric And Functional Analysis

, Volume 17, Issue 2, pp 468-490

First online:

On the Classification of Cartan Actions

  • Boris KalininAffiliated withDepartment of Mathematics & Statistics, University of South Alabama
  • , Ralf SpatzierAffiliated withDepartment of Mathematics, University of Michigan Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We study higher-rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by \(\mathbb{R}^{k}\) with k ≥ 3 whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic \(\mathbb{Z}^{k}\)-actions for k ≥ 3.

Keywords and phrases:

Hyperbolic dynamics Anosov actions rigidity

AMS Mathematics Subject Classification:

37D20 37C85 58D05