Comparative study of the adiabatic evolution of a nonlinear damped oscillator and a Hamiltonian generalized nonlinear oscillator

In this paper we study canonical equivalence and the identity of the geomet ric phases of dissipative and conservative 1D oscillators. We show that the quartic damped nonlinear oscillator is canonically equivalent to the linea r generalized harmonic oscillator for finite values of the damping paramete r whereas, in an appropriate weak damping limit, it becomes equivalent to t he quartic generalized oscillator. (C) 1998 Elsevier Science B.V.