English

Local Rigidity for Simultaneous Diophantine Translations on Tori of Arbitrary Dimension

Dynamical Systems 2018-04-30 v1

Abstract

We show that a smooth sufficiently small perturbation of a Zm\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.

Keywords

Cite

@article{arxiv.1804.10290,
  title  = {Local Rigidity for Simultaneous Diophantine Translations on Tori of Arbitrary Dimension},
  author = {Boris Petković},
  journal= {arXiv preprint arXiv:1804.10290},
  year   = {2018}
}

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13 pages