Consider a hyperbolic operator with principal symbol P. At a double characteristic point, the coefficient matrix of the Hamiltonian system associated with the quadratic form leading the Taylor expansion in the cotangent bundle is called the fundamental matrix. If the eigenvalues of the matrix are non-zero and real, then the operator is called effectively hyperbolic.
The author presents a method, using certain homogeneous canonical transformations, of reducing effectively hyperbolic operators to certain standard forms. He works out some examples which show connections with energy integrals. However the energy integral estimates appear elsewhere.