We have investigated the topological modification of an equilibrium with nested magnetic flux surfaces computed with the free boundary variational moments equilibrium code (VMEC) subject to an applied magnetic field perturbation. Magnetic field lines are traced in the domain interior to the plasma-vacuum interface either in the coordinates of the VMEC (s, u, v) or using canonical coordinates (psi, theta*, v) that allow a Hamiltonian description of the magnetic field lines. The perturbation models the effect of the magnetic Bur leakage from the saturated iron core of the JET device. Island formation around resonant surfaces near the boundary is observed, but these islands do not overlap. The Chirikov parameters and the Liapunov exponents are specifically calculated to verify this.