We construct an example of a Morse ℤ²-action which has rank one and whose centralizer contains elements which cannot be weakly approximated by the transformations of the action.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-2, author = {T. Downarowicz and J. Kwiatkowski}, title = {Weak Closure Theorem fails for $\mathbb{Z}$$^2$-actions}, journal = {Studia Mathematica}, volume = {151}, year = {2002}, pages = {115-125}, zbl = {1006.37005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-2} }
T. Downarowicz; J. Kwiatkowski. Weak Closure Theorem fails for ℤ²-actions. Studia Mathematica, Tome 151 (2002) pp. 115-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-2/