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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Regular Papers
Classification of Perturbations of Diophantine $\mathbb Z^m$ Actions
on Tori of Arbitrary Dimension
Boris Petković KTH Royal Institute of Technology,
100 44 Stockholm, Sweden
Аннотация:
We generalize results of Moser [17] on the circle to $\mathbb{T}^d$: we show that a smooth sufficiently small perturbation of a $\mathbb Z^m$ action, $m \geqslant 2$, on the torus $\mathbb{T}^d$ by simultaneously Diophantine translations, is smoothly conjugate to the unperturbed action under a natural condition on the rotation sets of diffeomorphisms isotopic to identity and we answer the question Moser posed in [17] by proving the existence of a continuum of $m$-tuples of simultaneously Diophantine vectors such that every element of the induced $\mathbb Z^m$ action is Liouville.
Ключевые слова:
KAM theory, simultaneously Diophantine translations, local rigidity, simultaneously
Diophantine approximations.
Поступила в редакцию: 11.11.2020 Принята в печать: 23.07.2021
Образец цитирования:
Boris Petković, “Classification of Perturbations of Diophantine $\mathbb Z^m$ Actions
on Tori of Arbitrary Dimension”, Regul. Chaotic Dyn., 26:6 (2021), 700–716
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1140 https://www.mathnet.ru/rus/rcd/v26/i6/p700
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