We give a positive answer to the problem of existence of smooth weakly mixing but not mixing flows on some surfaces. More precisely, on each compact connected surface whose Euler characteristic is even and negative we construct smooth weakly mixing flows which are disjoint in the sense of Furstenberg from all mixing flows and from all Gaussian flows.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-3,
author = {K. Fr\k aczek and M. Lema\'nczyk},
title = {On symmetric logarithm and some old examples in smooth ergodic theory},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {241-255},
zbl = {1047.37027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-3}
}
K. Frączek; M. Lemańczyk. On symmetric logarithm and some old examples in smooth ergodic theory. Fundamenta Mathematicae, Tome 177 (2003) pp. 241-255. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-3/