  We study the geometric phase factors underlying the classical and the
corresponding quantum dynamics of a driven nonlinear oscillator exhibiting
chaotic dynamics. For the classical problem, we compute the geometric phase
factors associated with the phase space trajectories using Frenet-Serret
formulation. For the corresponding quantum problem, the geometric phase
associated with the time evolution of the wave function is computed. Our
studies suggest that the classical geometric phase may be related to the the
difference in the quantum geometric phases between two neighboring eigenstates.
