nLab
Poisson pencil

If {,}\{,\} and {,}\{,\}' are two Poisson brackets on the same commutative algebra, or on the same manifold, then we say that they are compatible if any linear combination of these brackets a{,}+b{,}a\{,\}+b\{,\}' is again a Poisson bracket on the same commutative algebra or manifold. If so, all linear combination make a 2-parametric family of Poisson brackets. Such families are called Poisson pencils.

Created on May 24, 2011 at 14:47:11. See the history of this page for a list of all contributions to it.