Closed orbits of an Anosov flow and the fundamental group

Closed orbits of an Anosov flow and the fundamental group
HTML articles powered by AMS MathViewer

by Toshiaki Adachi PDF

Proc. Amer. Math. Soc. 100 (1987), 595-598 Request permission

We show that closed orbits of a transitive Anosov flow generate the fundamental group of the base manifold.

References

Toshiaki Adachi, Markov families for Anosov flows with an involutive action, Nagoya Math. J. 104 (1986), 55–62. MR 868437, DOI 10.1017/S0027763000022674
Toshiaki Adachi and Toshikazu Sunada, Homology of closed geodesics in a negatively curved manifold, J. Differential Geom. 26 (1987), no. 1, 81–99. MR 892032

Twisted Perron-Frobenius theorem and

-functions

Rufus Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429–460. MR 339281, DOI 10.2307/2373793
David Fried, Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helv. 57 (1982), no. 2, 237–259. MR 684116, DOI 10.1007/BF02565860

The zeta functions of Ruelle and selberg

William Parry and Mark Pollicott, The Chebotarov theorem for Galois coverings of Axiom A flows, Ergodic Theory Dynam. Systems 6 (1986), no. 1, 133–148. MR 837980, DOI 10.1017/S0143385700003333
Charles Pugh and Michael Shub, The $\Omega$-stability theorem for flows, Invent. Math. 11 (1970), 150–158. MR 287579, DOI 10.1007/BF01404608
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
Toshikazu Sunada, Geodesic flows and geodesic random walks, Geometry of geodesics and related topics (Tokyo, 1982) Adv. Stud. Pure Math., vol. 3, North-Holland, Amsterdam, 1984, pp. 47–85. MR 758647, DOI 10.2969/aspm/00310047