Asymptotic action and asymptotic winding number for area-preserving diffeomorphisms of the disk

Abstract

Given a compactly supported area-preserving diffeomorphism of the disk, we prove an integral formula relating the asymptotic action to the asymptotic winding number. As a corollary, we obtain a new proof of Fathi's integral formula for the Calabi homomorphism on the disk.

15 pages, 1 figure, V2. This version includes only minor editorial changes

Cited by in corpus (1)

• Hutchings' inequality for the Calabi invariant revisited with an application to pseudo-rotations