<p>The geometric misalignment between the rotor and stator is a key challenge in rotor systems, which may cause severe rub-impact and fatigue failure. Meanwhile, the deformation caused by the rub-impact can further affect the geometric alignment, resulting in a coupling effect. Therefore, this study investigates the dynamic model of the rotor system under the coupling effect of geometric eccentricity and rub-impact, considering the time-varying clearance caused by geometric eccentricity and the rub-impact faults. The global Poincaré mapping structure of various periodic attractors is constructed in the two-parameter plane. A method for calculating the dynamic rubbing rate of the rubbing rotor is proposed. The existence range of periodic motion and chaotic regions of the rotor system in the two-parameter space and the dynamic transition mechanism are discussed, and some potential dynamic behaviors and response characteristics are discovered. Finally, the accuracy of the numerical simulation results is verified through experiments. The results show that geometric eccentricity can lead to anisotropic rotor–stator clearance and affect the stability and dynamic bifurcation mechanism of the system. The bifurcation diagrams and basin of attraction in the multi-initial value domain indicate that the period saddle-node bifurcation can lead to multi-state coexistence, and these coexistence attraction domains will erode each other. The global dynamic behavior of the rotor system is fully revealed through the two-parameter mapping analysis, achieving effective matching of system parameters and initial values, thereby improving the dynamic performance and motion control strategy of the rotor system.</p>