an:00437588
Zbl 0783.58059
Sharp, Richard
Closed orbits in homology classes for Anosov flows
EN
Ergodic Theory Dyn. Syst. 13, No. 2, 387-408 (1993).
00015695
1993
j
37D99 37C10 37A99
closed orbit; winding cycles; \(L\)-functions; Anosov flows; homology
We consider transitive Anosov flows \(\varphi:M \to M\) and give necessary and sufficient conditions for every homology class in \(H_ 1(M,\mathbb{Z})\) to contain a closed \(\varphi\)-orbit. Under these conditions, we derive an asymptotic formula for the number of closed \(\varphi\)-orbits in a fixed homology class, generalizing a result of Katsuda and Sunada.
R.Sharp