Local rigidity of certain solvable group actions on tori

Abstract

In this paper, we study a local rigidity property of $\mathbb{Z}{⋉}_{\lambda }\mathbb{R}$ 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 proportional time change.

References in corpus (2)

• Rigidity of some abelian-by-cyclic solvable group actions on ${\mathbb{T}}^N$
• Lyapunov exponents and rigidity of Anosov automorphisms and skew products