Homology of Closed Orbits of Anosov Flows

1 January 1973

journal article
Published by JSTOR in Proceedings of the American Mathematical Society

Vol. 37 (1) , 297-300
https://doi.org/10.2307/2038751

Abstract

It is shown that for a volume preserving Anosov flow on a compact manifold the closed orbits span the first homology (with real coefficients). The proof uses the notion of asymptotic cycles and results concerning the space of invariant measures for hyperbolic flows.

Keywords

This publication has 7 references indexed in Scilit:

Ergodic Properties of Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature
Published by Taylor & Francis ,2020
Invariant Manifolds
Lecture Notes in Mathematics, 1977
Anosov Flows
American Journal of Mathematics, 1972
On the Space of Invariant Measures for Hyperbolic Flows
American Journal of Mathematics, 1972
Periodic Orbits for Hyperbolic Flows
American Journal of Mathematics, 1972
Diffeomorphisms with invariant line bundles
Inventiones Mathematicae, 1971
Asymptotic Cycles
Annals of Mathematics, 1957