On local rigidity of partially hyperbolic affine \(\mathbb{Z}^k\) actions

DOI10.1515/crelle-2016-0059zbMath1430.37031OpenAlexW2554832880MaRDI QIDQ2420200

Bassam Fayad, Danijela Damjanović

Publication date: 5 June 2019

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle-2016-0059

zbMATH Keywords

local rigiditypartially hyperbolic actions

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Groups as automorphisms of other structures (22F50)

Related Items

On simultaneous linearization of certain commuting nearly integrable diffeomorphisms of the cylinder, Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus, Dynamical systems. Abstracts from the workshop held July 11--17, 2021 (hybrid meeting), Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms, Classification of perturbations of Diophantine \(\mathbb{Z}^m\) actions on tori of arbitrary dimension, Transversal local rigidity of discrete abelian actions on Heisenberg nilmanifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Abelian actions with globally hypoelliptic leafwise Laplacian and rigidity
• Global rigidity of higher rank abelian Anosov algebraic actions
• On commuting circle mappings and simultaneous Diophantine approximations
• Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus
• Smooth linearization of commuting circle diffeomorphisms
• The first cohomology group, mixing and minimal sets of the commutative group of algebraic actions on a torus
• Rigidity for Anosov actions of higher rank lattices
• Affine Anosov actions
• Regularity of the composition operator in spaces of Hölder functions
• Rigidity of partially hyperbolic actions of property (T) groups
• Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices
• Local rigidity of affine actions of higher rank groups and lattices
• Diophantine approximations on submanifolds of Euclidean space
• Local rigidity of certain partially hyperbolic actions of product type
• Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne
• Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions
• The inverse function theorem of Nash and Moser
• Generalized implicit function theorems with applications to some small divisor problems, I