Some Anosov actions which are affine

2020/03/09 by de Almeida, Uira Noberto Matos
#Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2003.03883

Abstract

Following the works of Y. Benoist, P. Foulon and F. Labourie \citeBFL, and having in mind the standing conjecture about the algebricity of Anosov actions of ℝ^k, we propose some geometrical conditions which generalize the notion of contact structures and prove that Anosov actions associated with such structures are conjugated to an Affine action. We also construct two families of examples, the first one is algebraic in nature, and the second one imposes some dynamical conditions instead of geometrical ones.

Related

• Generalized k-contact structures
• Affine Anosov representations
• Anosov actions: minimality of foliations or suspension action
• There exist no contact Anosov diffeomorphisms
• Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds