Homotopic indivisibility of closed orbits of 3-dimensional Anosov flows
The author considers 3-dimensional Anosov flows. Closed orbits of such flows have excellent homotopic properties: they always represent non trivial, infinite order elements of the fundamental group. In the paper the author investigates homotopic divisibility of closed orbits of the flow. It is proved that given an Anosov flow \(\Phi\) in \(M^{3}\) so that its stable and unstable foliations are transversely orientable then any closed orbit \(\gamma\) of \(\Phi\) (traversed once) represents an indivisible element in the fundamental group of \(M\). In the non-orientable case the author proves that if a closed orbit \(\gamma\) is freely homotopic to \(\alpha^{n}\), where \(\alpha\) is a closed curve in \(M\), then \(|n |\leq 2\).
scientific article; zbMATH DE number 1033935