Centralizers of derived-from-Anosov systems on ${\mathbb{T}}^3$: rigidity versus triviality

Abstract

In this paper, we study the centralizer of a partially hyperbolic diffeomorphism on ${\mathbb{T}}^3$ which is homotopic to an Anosov automorphism, and we show that either its centralizer is virtually trivial or such diffeomorphism is smoothly conjugate to its linear part.

arXiv comment24 pages

References in corpus (5)

• Pointwise partial hyperbolicity in 3-dimensional nilmanifolds
• Global rigidity of higher rank Anosov algebraic actions
• Trivial centralizers for Axiom A diffeomorphisms
• Rigidity of measurable structure for Z^d-actions by automorphisms of a torus
• Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms

Cited by in corpus (2)

• Accessibility and centralizers for partially hyperbolic flows
• Centralizer classification and rigidity for some partially hyperbolic toral automorphisms