Geometric phase shifts under adiabatic parameter changes in classical dissipative systems

It is shown that a phenomenon analogous to Berry's phase and Hannay's angle occurs in dissipative systems. Adiabatic transport of a dissipative oscillatory system about a closed path in parameter space produces a geometric shift in the variable parametrizing the limit cycle. This quantity is written as the integral of a two-form over a surface bounded by the parameter-space loop.