An Integral Formula for the Volume Entropy with an Application to Rigidity

Abstract

where Bf M (x; r) is the ball of radius r centered at x in f M . It is proved by Manning [M] and Freire-Mañé [FM] that the limit exists and is independent of the center x 2 f M , v H, the topological entropy of the geodesic ‡ow on M , v = H if M has no conjugate points. There has been a lot of work on understanding the volume entropy of which we only… (More)

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