We present a numerical investigation of the ray dynamics in a paraxial
optical cavity when a ray splitting mechanism is present. The cavity is a
conventional two-mirror stable resonator and the ray splitting is achieved by
inserting an optical beam splitter perpendicular to the cavity axis. We show
that depending on the position of the beam splitter the optical resonator can
become unstable and the ray dynamics displays a positive Lyapunov exponent.Comment: 13 pages, 7 figures, 1 tabl