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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
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”, 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 Math. USSR-Izv.
\yr 1977
\vol 11
\issue 6
\pages 1195--1228
\mathnet{http://mi.mathnet.ru/eng/im2070}
\crossref{https://doi.org/10.1070/IM1977v011n06ABEH001766}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=488169}
\zmath{https://zbmath.org/?q=an:0376.58012|0399.58010}
Linking options:
  • https://www.mathnet.ru/eng/im2070
  • https://doi.org/10.1070/IM1977v011n06ABEH001766
  • https://www.mathnet.ru/eng/im/v41/i6/p1252
  • This publication is cited in the following 40 articles:
    1. Luís Barreira, Claudia Valls, SpringerBriefs in Mathematics, Spectra and Normal Forms, 2024, 1  crossref
    2. Edhin Franklin Mamani, “Geodesic flows of compact higher genus surfaces without conjugate points have expansive factors”, Nonlinearity, 37:5 (2024), 055019  crossref
    3. Alessandro Gaio Chimenton, José Barbosa Gomes, Rafael O. Ruggiero, “Reversibility at infinity and rigidity of Finsler manifolds without conjugate points”, Geom Dedicata, 217:2 (2023)  crossref
    4. Burns K. Matveev V.S., “Open Problems and Questions About Geodesics”, Ergod. Theory Dyn. Syst., 41:3 (2021), PII S0143385719000737, 641–684  crossref  isi
    5. Ludovic Rifford, Rafael Ruggiero, “On the stability conjecture for geodesic flows of manifolds without conjugate points”, Annales Henri Lebesgue, 4 (2021), 759  crossref
    6. César M. Silva, “Admissibility and generalized nonuniform dichotomies for discrete dynamics”, CPAA, 20:10 (2021), 3419  crossref
    7. Kiho Park, Tianyu Wang, “Multifractal analysis of geodesic flows on surfaces without focal points”, Dynamical Systems, 36:4 (2021), 656  crossref
    8. Alessandro Gaio Chimenton, José Barbosa Gomes, Rafael O. Ruggiero, “Gromov-hyperbolicity and transitivity of geodesic flows in n-dimensional Finsler manifolds”, Differential Geometry and its Applications, 68 (2020), 101588  crossref
    9. Gabriel Ponce, Régis Varão, SpringerBriefs in Mathematics, An Introduction to the Kolmogorov–Bernoulli Equivalence, 2019, 91  crossref
    10. Yaiza Canzani, Jeffrey Galkowski, “On the growth of eigenfunction averages: Microlocalization and geometry”, Duke Math. J., 168:16 (2019)  crossref
    11. Luís Barreira, Davor Dragičević, Claudia Valls, SpringerBriefs in Mathematics, Admissibility and Hyperbolicity, 2018, 75  crossref
    12. Vaughn Climenhaga, Yakov Pesin, “Building Thermodynamics for Non-uniformly Hyperbolic Maps”, Arnold Math J., 3:1 (2017), 37  crossref
    13. Luís Barreira, Lyapunov Exponents, 2017, 1  crossref
    14. Fei Liu, Fang Wang, “Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points”, Acta. Math. Sin.-English Ser., 32:4 (2016), 507  crossref
    15. Dan Jane, R.O.. Ruggiero, “Boundary of Anosov dynamics and evolution equations for surfaces”, Math. Nachr, 2014, n/a  crossref
    16. Katrin Gelfert, Barbara Schapira, “Pressures for geodesic flows of rank one manifolds”, Nonlinearity, 27:7 (2014), 1575  crossref
    17. Gang Liao, W.X.iang Sun, “Ergodic measures of geodesic flows on compact Lie groups”, Acta. Math. Sin.-English Ser, 29:9 (2013), 1781  crossref
    18. Antón.J..G. Bento, Cés.M.. Silva, “Nonuniform dichotomic behavior: Lipschitz invariant manifolds for ODEs”, Bulletin des Sciences Mathématiques, 2013  crossref
    19. Antón.J.. G. Bento, Cés.M.. Silva, “Generalized Nonuniform Dichotomies and Local Stable Manifolds”, J Dyn Diff Equat, 2013  crossref
    20. Luis Barreira, Davor Dragičević, Claudia Valls, “Lyapunov Functions and Cone Families”, J Stat Phys, 2012  crossref
    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
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    Abstract page:704
    Russian version PDF:196
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    References:87
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