Lyapunov exponents, path-integrals and forms

In this paper we use a path-integral approach to represent the Lyapunov exponents of both deterministic and stochastic dynamical systems. In both cases the relevant correlation functions are obtained from a (one-dimensional) supersymmetric field theory whose Hamiltonian, in the deterministic case, coincides with the Lie derivative of the associated Hamiltonian flow. The generalized Lyapunov exponents turn out to be related to the partition functions of the respective super-Hamiltonian restricted to the spaces of fixed form-degree