Local rigidity of higher rank non-abelian action on tours

2014/05/29 by Zhenqi Jenny Wang, Wang, Zhenqi Jenny
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1405.7737

arxiv created 2014/05/29 · arxiv updated 2014/06/02

Abstract

In this paper, we show local smooth rigidity for higher rank ergodic nilpotent action by toral automorphisms and prove the existence of such action on any torus TN for any even N ? 6. We also give examples of smooth rigidity of actions having rank-one factors. The method is a generalization of the KAM (Kolmogorov-Arnold-Moser) iterative scheme.

Related

• KAM rigidity for partially hyperbolic affine Z^k actions on the torus with a rank one factor
• Global rigidity of certain abelian actions by toral automorphisms
• Local rigidity of higher rank partially hyperbolic algebraic actions
• Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions
• Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds