Integrability versus topology of configuration manifolds and domains of possible motions

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73950We establish a generic sufficient condition for a compact $n$-dimensional manifold bearing an integrable geodesic flow to be the $n$-torus. As a complementary result, we show that in the case of domains of possible motions with boundary, the first Betti number of the domain of possible motions may be arbitrarily large.Dynamical Systems37J30, 37J35Integrability versus topology of configuration manifolds and domains of possible motionstext