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An area-preserving diffeomorphism of an annulus has an "action function"which measures how the diffeomorphism distorts curves. The average value of theaction function over the annulus is known as the Calabi invariant of thediffeomorphism, while the average value of the action function over a periodicorbit of the diffeomorphism is the mean action of the orbit. If anarea-preserving annulus diffeomorphism is a rotation near the boundary of theannulus, and if its Calabi invariant is less than the maximum boundary value ofthe action function, then we show that the infimum of the mean action over allperiodic orbits of the diffeomorphism is less than or equal to its Calabiinvariant.

Mean action of periodic orbits of area-preserving annulus diffeomorphisms