On a certain class of dynamical systems on the torus with rational rotation number

For system (1), the authors solve the problem of the existence of trajectories given by the linear equation y ≡ μx + y ₀ (mod 2π), μ ≥ 0, y ₀ ∈ ℝ, and in the case where such trajectories exist, they perform a complete qualitative study of the system on the two-dimensional torus under certain conditions. Translated From Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics And Its Applications), Vol. 53, Suzdal Conference-2006, Part 1, 2008.