Abstract
where B(x,R) is the ball of radius R around a fixed point x in the universal cover X. (For noncompact M , see Section 6.2.) The number h(g) is independent of the choice of x, and equals the topological entropy of the geodesic flow on (M, g) when the curvature K(g) satisfies K(g) ≤ 0 (see [Ma]). Note that while the volume Vol(M, g) is not invariant under scaling the metric g, the normalized entropy
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