## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

We prove that for a dense $G_{\delta}$ of shift-invariant measures
on $A^{\ZZ^d}$, all $d$ shifts have purely singular continuous spectrum
and give a new proof that in the weak topology of measure preserving $\ZZ^d$
transformations, a dense $G_{\delta}$ is generated by transformations
with purely singular continuous spectrum.
We also give new examples of smooth unitary cocycles over an
irrational rotation which have purely singular continuous spectrum.
Quantitative weak mixing properties are related by results of Strichartz and
Last to spectral properties of the unitary Koopman operators.

keywords:
spectral theory
,
invariant measures
,
singular continuous spectrum.
,
mixing
,
Ergodic theory

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]