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Closed orbits of an Anosov flow and the fundamental group


Author: Toshiaki Adachi
Journal: Proc. Amer. Math. Soc. 100 (1987), 595-598
MSC: Primary 58F15; Secondary 58F22
DOI: https://doi.org/10.1090/S0002-9939-1987-0891171-5
MathSciNet review: 891171
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Abstract: We show that closed orbits of a transitive Anosov flow generate the fundamental group of the base manifold.


References [Enhancements On Off] (What's this?)

  • [1] T. Adachi, Markov families for Anosov flows with an involutive action, Nagoya Math. J. 104 (1986), 55-62. MR 868437 (88b:58108)
  • [2] T. Adachi and T. Sunada, Homology of closed geodesics in a negatively curved manifold, J. Differential Geom. (to appear). MR 892032 (88g:58149)
  • [3] -, Twisted Perron-Frobenius theorem and $ L$-functions, J. Funct. Anal. (to appear).
  • [4] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429-460. MR 0339281 (49:4041)
  • [5] D. Fried, Flow equivalence, hyperbolic systems and new zeta function for flows, Comment. Math. Helv. 57 (1982), 237-259. MR 684116 (84g:58083)
  • [6] -, The zeta functions of Ruelle and selberg. I (preprint).
  • [7] W. Parry and M. Pollicott, The Chebotarev theorem for Galois coverings of Axiom A flow, Ergodic Theory Dynamical Systems 6 (1986), 133-148. MR 837980 (88k:58124)
  • [8] C. Pugh and M. Shub, $ \Omega $-stability theorem for flows, Invent. Math. 11 (1970), 150-158. MR 0287579 (44:4782)
  • [9] S. Smale, Differential dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 0228014 (37:3598)
  • [10] T. Sunada, Geodesic flows and geodesic random walks, Geometry of Geodesics and Related Topics, Studies in Pure Math., no. 3, North-Holland, Amsterdam and New York, 1984, pp. 47-86. MR 758647 (86i:58104)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0891171-5
Keywords: Anosov flow, closed orbit, fundamental group, oriented graph
Article copyright: © Copyright 1987 American Mathematical Society

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