Hamiltonian reformulation and pairing of Lyapunov exponents for Nosé-Hoover dynamics

The Nos\'eHamiltonian is adapted, leading to a derivation of the Nos\'e-Hoover equations of motion which does not involve time transformations, and in which the degree of freedom corresponding to the external reservoir is treated on the same footing as those of the rest of the system. In this form it is possible to prove the conjugate pairing rule for Lyapunov exponents of this system.