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Mathematics of the USSR-Izvestiya, 1977, Volume 11, Issue 6, Pages 1195–1228
DOI: https://doi.org/10.1070/IM1977v011n06ABEH001766
(Mi im2070)
 

This article is cited in 40 scientific papers (total in 40 papers)

Geodesic flows on closed Riemannian manifolds without focal points

Ya. B. Pesin
References:
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
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1977, Volume 41, Issue 6, Pages 1252–1288
Bibliographic databases:
UDC: 517.9
MSC: Primary 28A65, 58F15, 34C35; Secondary 53C20
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
\Bibitem{Pes77}
\by Ya.~B.~Pesin
\paper Geodesic flows on closed Riemannian manifolds without focal points
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 6
\pages 1252--1288
\mathnet{http://mi.mathnet.ru/im2070}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=488169}
\zmath{https://zbmath.org/?q=an:0376.58012|0399.58010}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 6
\pages 1195--1228
\crossref{https://doi.org/10.1070/IM1977v011n06ABEH001766}
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  • This publication is cited in the following 40 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:644
    Russian version PDF:183
    English version PDF:74
    References:71
    First page:1
     
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