Transversal local rigidity of discrete abelian actions on Heisenberg nilmanifolds

DOI10.1017/etds.2021.79zbMath1504.37037arXiv2003.00338OpenAlexW3006802263WikidataQ114118702 ScholiaQ114118702MaRDI QIDQ5868364

Danijela Damjanović, James Tanis

Publication date: 20 September 2022

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.00338

zbMATH Keywords

Heisenberg nilmanifoldsabelian actionslocal rigity

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Rigidity results (53C24) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Group actions on manifolds and cell complexes in low dimensions (57M60)

Cites Work

• Abelian actions with globally hypoelliptic leafwise Laplacian and rigidity
• Cocycle rigidity and splitting for some discrete parabolic 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
• Local rigidity of homogeneous parabolic actions: I. A model case
• Equidistribution for higher-rank abelian actions on Heisenberg nilmanifolds
• Classification of perturbations of Diophantine \(\mathbb{Z}^m\) actions on tori of arbitrary dimension
• Rigidity of some abelian-by-cyclic solvable group actions on \({\mathbb{T}}^N\)
• Cohomological equation and cocycle rigidity of discrete parabolic actions in some higher-rank Lie groups
• Local rigidity of higher rank homogeneous abelian actions: a complete solution via the geometric method
• On local rigidity of partially hyperbolic affine \(\mathbb{Z}^k\) actions
• Cohomological equation and cocycle rigidity of discrete parabolic actions
• Perturbations of Smooth Actions with Nontrivial Cohomology
• Local Rigidity of Partially Hyperbolic Actions. II: The Geometric Method and Restrictions of Weyl Chamber Flows on SL(n, R)/
• Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions
• The inverse function theorem of Nash and Moser
• Heisenberg Manifolds and Theta Functions
• Equidistribution of nilflows and applications to theta sums