Local rigidity of certain solvable group actions on tori

Qiao Liu

doi:10.3934/dcds.2020269

Article Contents

2021, Volume 41, Issue 2: 553-567. Doi: 10.3934/dcds.2020269

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Local rigidity of certain solvable group actions on tori

Qiao Liu

Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA

Received: January 2020

Revised: June 2020

Early access: July 2020

Published: February 2021

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Abstract

In this paper, we study a local rigidity property of $ \mathbb Z \ltimes_\lambda \mathbb R $ affine action on tori generated by an irreducible toral automorphism and a linear flow along an eigenspace. Such an action exhibits a weak version of local rigidity, i.e., any smooth perturbations close enough to an affine action is smoothly conjugate to the affine action up to constant time change.

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Mathematics Subject Classification: Primary:37C85;Secondary:57S25.

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References

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