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Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds. (English) Zbl 0725.58026
Let M be a simply connected negatively curved manifold, \(\partial M\) its sphere at infinity. There exists a natural one-to-one correspondence between the invariant measures of the geodesic flow on the unit tangent bundle and the measures on \(\partial^ 2M=(\partial M\times \partial M\setminus diagonal).\) Using this correspondence, the author gives new constructions of the maximal entropy and the harmonic invariant measures of the geodesic flow.

MSC:
37A99 Ergodic theory
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
58J65 Diffusion processes and stochastic analysis on manifolds
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