  We prove that the Calabi invariant of a $C^1$ pseudo-rotation of the unit
disk, that coincides with a rotation on the unit circle, is equal to its
rotation number. This result has been shown some years ago by Michael Hutchings
(under very slightly stronger hypothesis). While the original proof used
Embedded Contact Homology techniques, the proof of this article uses generating
functions and the dynamics of the induced gradient flow.
