We have mapped the emission from atomic hydrogen at 21 cm from the galaxy NGC 3783 with the Australia Telescope Compact Array. Our main results are: a) the HI morphology is irregular and perturbed, gathered in three blobs apparently unrelated to the optical morphology; b) the observed HI velocity distribution indicates a normal disk in differential rotation with a constant velocity out to a radius of 160 (30 kpc), c) the inclination of the disk is about 25 deg with the kinematic major axis at a position angle slightly different from that of the stellar bar, d) the HI mass inside a radius of 18 is only 2.1 10^7 Msun, the total HI mass within 180 is 1.1 10^9 Msun and the dynamical mass is 2 10^{11} Msun. The bulk of the gas in NGC 3783 is outside the diameter of the stellar bar; e) Numerical simulations of the gas flow in the barred potential derived from the red image indicate that the pattern speed is Omega_p = 38 km/s/kpc: the ring of Halpha emitting regions encircling the bar would then correspond to UHR, and the Halpha accumulation in the center to a nuclear ring. Various possibilities are discussed to account for the active nucleus fuelling.
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