The Teichmüller flow is Hamiltonian

Howard Masur
1995 Proceedings of the American Mathematical Society  
It is shown that the Teichmuller flow on the cotangent bundle over Teichmuller space coincides with the Hamiltonian flow defined by the function which gives the length of a cotangent vector.
doi:10.1090/s0002-9939-1995-1283559-2 fatcat:hbennvpfsba65kfu3xrgxqledu