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Regular and Chaotic Dynamics, 2018, Volume 23, Issue 1, Pages 12–25
DOI: https://doi.org/10.1134/S1560354718010021
(Mi rcd305)
 

This article is cited in 8 scientific papers (total in 8 papers)

Local Rigidity of Diophantine Translations in Higher-dimensional Tori

Nikolaos Karaliolios

Imperial College London, South Kensington Campus, London, SW7 2AZ, UK
Citations (8)
References:
Abstract: We prove a theorem asserting that, given a Diophantine rotation $\alpha $ in a torus $\mathbb{T} ^{d} \equiv \mathbb{R} ^{d} / \mathbb{Z} ^{d}$, any perturbation, small enough in the $C^{\infty}$ topology, that does not destroy all orbits with rotation vector $\alpha$ is actually smoothly conjugate to the rigid rotation. The proof relies on a KAM scheme (named after Kolmogorov – Arnol'd – Moser), where at each step the existence of an invariant measure with rotation vector $\alpha$ assures that we can linearize the equations around the same rotation $\alpha$. The proof of the convergence of the scheme is carried out in the $C^{\infty}$ category.
Keywords: KAM theory, quasi-periodic dynamics, Diophantine translations, local rigidity.
Funding agency Grant number
European Research Council 339523 RGDD
This work was funded by the ERC AdG grant no 339523 RGDD.
Received: 11.08.2017
Accepted: 01.12.2017
Bibliographic databases:
Document Type: Article
MSC: 37C05, 37C55
Language: English
Citation: Nikolaos Karaliolios, “Local Rigidity of Diophantine Translations in Higher-dimensional Tori”, Regul. Chaotic Dyn., 23:1 (2018), 12–25
Citation in format AMSBIB
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\by Nikolaos Karaliolios
\paper Local Rigidity of Diophantine Translations in Higher-dimensional Tori
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 1
\pages 12--25
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:216
    References:47
     
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