Reduced Tangent Dynamics and Lyapunov Spectrum for Hamiltonian Systems

A reduced formulation of tangent dynamics and the Lyapunov spectrum for a Hamiltonian system using its underlying symplectic symmetry is developed. It applies to a symplectic dynamical system of any dimension and leads to differential equations dealing directly with the characteristic exponents. These equations do not contain exponentially growing quantities nor require any orthonormality maintenance, and they are capable of dealing with degeneracies in the spectrum.