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Transversal local rigidity of discrete abelian actions on Heisenberg nilmanifolds

Part of: Dynamical systems with hyperbolic behavior Smooth dynamical systems: general theory

Published online by Cambridge University Press:  04 August 2021

DANIJELA DAMJANOVIĆ  and
JAMES TANIS
DANIJELA DAMJANOVIĆ
Affiliation:
Department of Mathematics, Kungliga Tekniska Högskolan, Lindstedtsvägen 25, 10044 Stockholm, Sweden (e-mail: ddam@kth.se)
JAMES TANIS*
Affiliation:
The MITRE Corporation, McLean, VA 22102, USA
*
e-mail: jhtanis@mitre.org
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Abstract

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.

Keywords

local rigityabelian actionsHeisenberg nilmanifolds

MSC classification

Primary: 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification 37C85: Dynamics of group actions other than ${bf Z}$ and ${bf R}$, and foliations 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 10 , October 2022 , pp. 3111 - 3151
Copyright
© The MITRE Corporation, 2021. Published by Cambridge University Press

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References

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