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On the ergodicity of the Weyl sums cocycle

100%

Fayad B.

Acta Arithmetica

2006

tom 125

nr 4

305-316

On the convergence to 0 of mₙξmod 1

84%

Fayad B., Thouvenot J.-P.

Acta Arithmetica

2014

tom 165

nr 4

327-332

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.

Ograniczanie wyników

2 Acta Arithmetica

2 Fayad B.

1 Thouvenot J.-P.

1 2014

1 2006

Wyniki wyszukiwania

On the ergodicity of the Weyl sums cocycle

On the convergence to 0 of mₙξmod 1