## Spectral properties of ergodic dynamical systems conjugate to their composition squares

### Volume 107 / 2007

Colloquium Mathematicum 107 (2007), 99-118
MSC: Primary 37A05; Secondary 28D05.
DOI: 10.4064/cm107-1-10

#### Abstract

Let $S$ and $T$ be automorphisms of a standard Borel probability space. Some ergodic and spectral consequences of the equation $ST=T^2S$ are given for $T$ ergodic and also when $T^n=I$ for some $n>2$. These ideas are used to construct examples of ergodic automorphisms $S$ with oscillating maximal spectral multiplicity function. Other examples illustrating the theory are given, including Gaussian automorphisms having simple spectra and conjugate to their squares.