|
This article is cited in 40 scientific papers (total in 40 papers)
Geodesic flows on closed Riemannian manifolds without focal points
Ya. B. Pesin
Abstract:
In this paper it is proved that a geodesic flow on a two-dimensional compact manifold of genus greater than 1 with Riemannian metric without focal points is isomorphic with a Bernoulli flow. This result generalizes to the multidimensional case. The proof is based on establishing some metric properties of flows with nonzero Ljapunov exponents (the $K$-property, etc.), and also the construction of horospheres and leaves on a very wide class of Riemannian manifolds, together with a study of some of their geometric properties.
Bibliography: 24 titles.
Received: 16.09.1976
Citation:
Ya. B. Pesin, “Geodesic flows on closed Riemannian manifolds without focal points”, Izv. Akad. Nauk SSSR Ser. Mat., 41:6 (1977), 1252–1288; Math. USSR-Izv., 11:6 (1977), 1195–1228
Linking options:
https://www.mathnet.ru/eng/im2070https://doi.org/10.1070/IM1977v011n06ABEH001766 https://www.mathnet.ru/eng/im/v41/i6/p1252
|
Statistics & downloads: |
Abstract page: | 644 | Russian version PDF: | 183 | English version PDF: | 74 | References: | 71 | First page: | 1 |
|