2 results
Non-rigidity of partially hyperbolic abelian
$C^1$-actions on tori
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 45 / Issue 2 / February 2025
- Published online by Cambridge University Press:
- 09 September 2024, pp. 573-594
- Print publication:
- February 2025
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We prove that every genuinely partially hyperbolic
$\mathbb {Z}^r$-action by toral automorphisms can be perturbed in 
$C^1$-topology, so that the resulting action is continuously conjugate, but not 
$C^1$-conjugate, to the original one.
Transversal local rigidity of discrete abelian actions on Heisenberg nilmanifolds
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 42 / Issue 10 / October 2022
- Published online by Cambridge University Press:
- 04 August 2021, pp. 3111-3151
- Print publication:
- October 2022
-
- Article
- Export citation
-
In this paper we prove a perturbative result for a class of
${\mathbb Z}^2$
actions on Heisenberg nilmanifolds that have Diophantine properties. Along the way we prove cohomological rigidity and obtain a tame splitting for the cohomology with coefficients in smooth vector fields for such actions.
