2018/10/11 by Morgan Weiler, Weiler, Morgan · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1810.05091
An area-preserving diffeomorphism of an annulus has an "action function"\nwhich measures how the diffeomorphism distorts curves. The average value of the\naction function over the annulus is known as the Calabi invariant of the\ndiffeomorphism, while the average value of the action function over a periodic\norbit of the diffeomorphism is the mean action of the orbit. If an\narea-preserving annulus diffeomorphism is a rotation near the boundary of the\nannulus, and if its Calabi invariant is less than the maximum boundary value of\nthe action function, then we show that the infimum of the mean action over all\nperiodic orbits of the diffeomorphism is less than or equal to its Calabi\ninvariant.\n