Geodesic
Topological entropy of geodesic flows on simply connected manifolds, and related topics
Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 517-535

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Lower estimates are obtained for the topological entropy of geodesic flows on simply connected manifolds. The estimates involve two constants; one depends on the homotopy type of the manifold only, and the other, introduced in this paper, on the properties of the metric in question. Some related topics are studied. 
@article{IM2_1997_61_3_a1,
     author = {I. K. Babenko},
     title = {Topological entropy of geodesic flows on simply connected manifolds, and related topics},
     journal = {Izvestiya. Mathematics },
     pages = {517--535},
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     volume = {61},
     number = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a1/}
}
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I. K. Babenko. Topological entropy of geodesic flows on simply connected manifolds, and related topics. Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 517-535. http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a1/