Abstract
In this paper we show that the geodesic flow on a compact locally symmetric space of nonpositive curvature has a unique invariant measure of maximal entropy. As an application to dynamics we show that closed geodesics are uniformly distributed with respect to this measure. Furthermore, we prove that the volume entropy is minimized at a compact locally symmetric space of nonpositive curvature among all conformally equivalent metrics with the same total volume.
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Knieper, G. The uniqueness of the maximal measure for geodesic flows on symmetric spaces of higher rank. Isr. J. Math. 149, 171–183 (2005). https://doi.org/10.1007/BF02772539
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DOI: https://doi.org/10.1007/BF02772539