Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings

This monograph is devoted to the properties of infinite (either in one direction or in both directions) curves without self-intersections on closed surfaces. The properties considered are those that are exhibited when the curves are lifted to the universal covering and are associated with the asymptotic behavior of the lifted curves at infinity; these properties mainly manifest themselves when the curves are compared with geodesics or with curves of constant geodesic curvature. The approach described can be applied to the trajectories of flows (which leads to a far-reaching generalization of the Poincaré rotation numbers) and to the leaves of foliations and laminations.