  We study the space of measured laminations ML on a closed surface from the
valuative point of view. We introduce and study a notion of Newton polytope for
an algebraic function on the character variety. We prove for instance that
trace functions have unit coefficients at the extremal points of their Newton
polytope. Then we provide a definition of tangent space at a valuation and show
how the Goldman Poisson bracket on the character variety induces a symplectic
structure on this valuative model for ML. Finally we identify this symplectic
space with previous constructions due to Thurston and Bonahon.
