Basic ergodic properties of the ELF class of automorphisms, i.e. of the class of ergodic automorphisms whose weak closure of measures supported on the graphs of iterates of T consists of ergodic self-joinings are investigated. Disjointness of the ELF class with: 2-fold simple automorphisms, interval exchange transformations given by a special type permutations and time-one maps of measurable flows is discussed. All ergodic Poisson suspension automorphisms as well as dynamical systems determined by stationary ergodic symmetric α-stable processes are shown to belong to the ELF class.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-1-3,
author = {Y. Derriennic and K. Fr\k aczek and M. Lema\'nczyk and F. Parreau},
title = {Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings},
journal = {Colloquium Mathematicae},
volume = {111},
year = {2008},
pages = {81-115},
zbl = {1142.37005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-1-3}
}
Y. Derriennic; K. Frączek; M. Lemańczyk; F. Parreau. Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings. Colloquium Mathematicae, Tome 111 (2008) pp. 81-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-1-3/