Some examples of cocycles with simple continuous singular spectrum

• Autorzy: K. Frączek
• Języki publikacji: EN

Abstrakty

EN

We study spectral properties of Anzai skew products $T_{φ}: 𝕋² → 𝕋²$ defined by
$T_{φ}(z,ω) = (e^{2πiα}z,φ(z)ω)$,
where α is irrational and φ: 𝕋 → 𝕋 is a measurable cocycle. Precisely, we deal with the case where φ is piecewise absolutely continuous such that the sum of all jumps of φ equals zero. It is shown that the simple continuous singular spectrum of $T_{φ}$ on the orthocomplement of the space of functions depending only on the first variable is a "typical" property in the above-mentioned class of cocycles, if α admits a sufficiently fast approximation.

Kategorie tematyczne

• 37A05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 146
• Numer: 1
• Strony: 1-13

Daty

wydano

2001

Twórcy

autor

K. Frączek

• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/sm146-1-1