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Local rigidity of certain solvable group actions on tori

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  • 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.

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


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