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We have investigated magnetic vortex dynamics in the frequency and time domains using time-resolved Kerr microscopy. A synchronous detection technique allows us to probe a single disk over a large dynamic range (four orders of magnitude in excitation power). Three regimes are identified. At low excitation amplitudes, the gyrotropic motion of the vortex is strongly modified by the presence of point-like defects. As the amplitude increases, the system passes through a depinning transition, above which the gyroptropic dynamics are determined by the magnetostatic potential of the disk. At very high amplitudes, the assumption of a rigid vortex core breaks down and the dynamics are dominated by successive reversals of the vortex core polarity.