We present observations of the nearby barred starburst galaxy M83 (NGC 5236), with the new Fabry-Perot interferometer GHαFaS mounted on the 4.2 m William Herschel Telescope on La Palma. The unprecedented high-resolution observations, of 16 pc FWHM-1, of the Hα-emitting gas cover the central 2 kpc of the galaxy. The velocity field displays the dominant disk rotation with signatures of gas inflow from kpc scales down to the nuclear regions. At the inner inner Lindblad resonance radius of the main bar and centered at the dynamical center of the main galaxy disk, a nuclear (5.5 +/- 0.9) × 108 Msolar rapidly rotating disk with scale length of 60+/-20 pc has formed. The nuclear starburst is found in the vicinity as well as inside this nuclear disk, and our observations confirm that gas spirals in from the outer parts to feed the nuclear starburst, giving rise to several star formation events at different epochs, within the central 100 pc radius of M83.