Examples of Poisson structures with isolated non-symplectic points are constructed from classical r-matrices.
@article{bwmeta1.element.bwnjournal-article-bcpv51z1p11bwm, author = {Zakrzewski, S.}, title = {Poisson structures on $$\mathbb{R}$^{2N}$ having only two symplectic leaves: the origin and the rest}, journal = {Banach Center Publications}, volume = {51}, year = {2000}, pages = {11-13}, zbl = {0992.53061}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p11bwm} }
Zakrzewski, S. Poisson structures on $ℝ^{2N}$ having only two symplectic leaves: the origin and the rest. Banach Center Publications, Tome 51 (2000) pp. 11-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p11bwm/
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