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arXiv · 1804.10290

Local Rigidity for Simultaneous Diophantine Translations on Tori of Arbitrary Dimension

Boris Petković
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Abstract

We show that a smooth sufficiently small perturbation of a $\mathbb Z^m$ action on the torus by simultaneously Diophantine translations, is smoothly conjugate to the unperturbed action under a natural condition on the rotation sets. This generalizes recent result of Karaliolios [4] of the action generators to higher rank abelian actions, and the result of Moser [8] to higher dimensional tori.

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Boris Petković. 2018-04-26. Local Rigidity for Simultaneous Diophantine Translations on Tori of Arbitrary Dimension. https://arxiv.org/abs/1804.10290

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