Let S and T be automorphisms of a standard Borel probability space. Some ergodic and spectral consequences of the equation ST = T²S are given for T ergodic and also when Tⁿ = 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-10,
author = {Geoffrey R. Goodson},
title = {Spectral properties of ergodic dynamical systems conjugate to their composition squares},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {99-118},
zbl = {1131.37004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-10}
}
Geoffrey R. Goodson. Spectral properties of ergodic dynamical systems conjugate to their composition squares. Colloquium Mathematicae, Tome 107 (2007) pp. 99-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-10/