2 results
Non-rigidity of partially hyperbolic abelian
$C^1$-actions on tori
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- Journal:
- Ergodic Theory and Dynamical Systems , First View
- Published online by Cambridge University Press:
- 09 September 2024, pp. 1-22
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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
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 42 / Issue 10 / October 2022
- Published online by Cambridge University Press:
- 04 August 2021, pp. 3111-3151
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- October 2022
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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.
