Log-canonical coordinates provides the simplest from to which a quadratic Poisson bracket can be reduced via a rational transformation. Such coordinates play an important role in a construction of cluster structures on Poisson varieties. We present a construction of log-canonical charts on Poisson- Lie groups and Poisson homogeneous spaces associated with R-matrices arising in the Belavin-Drinfeld classification. The key ingredient is a Poisson map from a simple Lie group equipped with the standard Poisson-Lie group to the same group equipped with a nontrivial Belavin-Drinfeld Poisson bracket. This is a joint project with M. Shapiro and A. Vainshtein.
