Topological classification for linear extensions of minimal flows

In this paper the problem of tological classification for the skew-product flows of the form
$$F^t(\varphi,\theta)\,=\,(\varphi_t,F^t_\varphi(\theta))({\rm mod}2\pi),$$
where $\{\varphi_t\}$ is minimal flow on compact metric space, the fiber map $F^t_\varphi$ is an linear automorphism $R^n$ is concidering. The necessary and sufficient conditions of the equivalence of linear hyperbolic extensions is giving.