Teichmüller spaces as degenerated symplectic leaves in Dubrovin-Ugaglia Poisson manifolds

► We study certain symplectic leaves in the Poisson algebra of Stokes matrices. ► This Poisson algebra is given by the Dubrovin-Ugaglia bracket. ► This coincides with the Goldman bracket in the Teichmüller theory. ► We prove that the Teichmüller spaces belong to degenerated symplectic leaves. ► Their complex dimension is equal to the real dimension of the Teichmüller space.