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heisenberg nilmanifolds

Ergodic Theory and Dynamical Systems (1)

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1 results

Transversal local rigidity of discrete abelian actions on Heisenberg nilmanifolds
Part of
- Smooth dynamical systems: general theory
- Dynamical systems with hyperbolic behavior
DANIJELA DAMJANOVIĆ, JAMES TANIS
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
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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.