Conformally symplectic dynamics and symmetry of the Lyapunov spectrum

Abstract. A generalization of the Hamiltonian formalism is studied and the sym-metry of the Lyapunov spectrum established for the resulting systems. The formalism is applied to the Gausssian isokinetic dynamics of interacting particles with hard core collisions and other systems. x0. Introduction. We study the symmetry of the Lyapunov spectrum in systems more general than Hamiltonian but closely related to the symplectic formalism. We call these systems conformally Hamiltonian. They are determined by a non-degenerate 2-form on the phase space and a function H, called again a Hamiltonian. The form is no