Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We show that for any irrational number α and a sequence ${m_l}_{l∈ℕ}$ of integers such that $lim_{l→∞} |||m_l α||| = 0$, there exists a continuous measure μ on the circle such that $lim_{l→∞} ∫_{𝕋} |||m_l θ||| dμ(θ) = 0$. This implies that any rigidity sequence of any ergodic transformation is a rigidity sequence for some weakly mixing dynamical system.
On the other hand, we show that for any α ∈ ℝ - ℚ, there exists a sequence ${m_l}_{l∈ℕ}$ of integers such that $|||m_l α||| → 0$ and such that $m_l θ[1]$ is dense on the circle if and only if θ ∉ ℚα + ℚ.
On the other hand, we show that for any α ∈ ℝ - ℚ, there exists a sequence ${m_l}_{l∈ℕ}$ of integers such that $|||m_l α||| → 0$ and such that $m_l θ[1]$ is dense on the circle if and only if θ ∉ ℚα + ℚ.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
327-332
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- IMJ-PRG, CNRS UMR 7586, UP7D-Campus Grand Moulin, Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, France
autor
- LPMA, Université Pierre et Marie Curie, 4 pl. Jussieu, 75252 Paris, France
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-4-2