For every irrational rotation we construct a coboundary which is continuous except at a single point where it has a jump, is nondecreasing, and has zero derivative almost everywhere.
@article{bwmeta1.element.bwnjournal-article-smv126i3p253bwm, author = {Dalibor Voln\'y}, title = {BV coboundaries over irrational rotations}, journal = {Studia Mathematica}, volume = {122}, year = {1997}, pages = {253-271}, zbl = {0890.28011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv126i3p253bwm} }
Volný, Dalibor. BV coboundaries over irrational rotations. Studia Mathematica, Tome 122 (1997) pp. 253-271. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv126i3p253bwm/
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