GAFA Geometric And Functional Analysis

, Volume 17, Issue 2, pp 468–490

On the Classification of Cartan Actions

Article

Abstract.

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 

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Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of South AlabamaMobileUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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