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Dynamics Seminar
October 24, 2007

Ian Biringer
University of Chicago

A Combinatorial Property of Isometric Z-Actions and Geodesic Flow

A classical theorem in combinatorics says that the set of points on the circle obtained by rotating a point by any prescribed angle a given number of times divides the circle into segments of at most 3 different lengths. We generalize this result to isometries of Riemannian manifolds with sectional curvature bounds, and use a similar idea involving geodesic flow to give a combinatorial characterization of surfaces with all geodesics simple, closed and of equal length. Joint with Benjamin Schmidt.

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