# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Some examples of cocycles with simple continuous singular spectrum

### Tom 146 / 2001

Studia Mathematica 146 (2001), 1-13 MSC: Primary 37A05. DOI: 10.4064/sm146-1-1

#### Streszczenie

We study spectral properties of Anzai skew products $T_{\varphi }:{\mathbb T}^2\rightarrow {\mathbb T}^2$ defined by $$T_{\varphi }(z,\omega )=(e^{2\pi i\alpha }z,\varphi (z) \omega ),$$ where $\alpha$ is irrational and $\varphi :{\mathbb T}\rightarrow {\mathbb T}$ is a measurable cocycle. Precisely, we deal with the case where $\varphi$ is piecewise absolutely continuous such that the sum of all jumps of $\varphi$ equals zero. It is shown that the simple continuous singular spectrum of $T_{\varphi }$ 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 $\alpha$ admits a sufficiently fast approximation.

#### Autorzy

• K. Fr/aczekFaculty of Mathematics and Computer Science
Nicholas Copernicus University
Chopina 12/18
87-100 Toru/n, Poland
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek