Spray simulation. II
In part I of this paper [Russ. Math. 36, No. 6, 60-66 (1992); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1992, No. 6(361), 63-70 (1992; Zbl 0778.58056)] and in [Sov. Math., Dokl. 44, No. 3, 474-478 (1992); translation from Dokl. Akad. Nauk SSSR 320, No. 3, 531-535 (1991; Zbl 0776.58029)], the author has constructed a spray model of an arbitrary quasigeodesic flow (QF), i.e., a second order ordinary differential equation. As well there had been revealed applications of such a simulation. In particular, there had been defined an exponential mapping of an arbitrary QF and obtained results on exponential properties and on the two-end problem for QF. In the present article we apply classical results on differential geometry of spray spaces (or, what is the same, of general spaces of geodesics) in order to study pointwise isomorphisms of QF (Sections 2 and 3 of the article) and to examine the QF triviality problem (see Section 5).
scientific article; zbMATH DE number 822626