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This paper employs a hybrid numerical method combining the differential transformation method and the finite difference method to study the dynamic behavior of a rigid rotor supported by a micro gas journal bearing system. The analytical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and quasi-periodic responses of the rotor center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass is increased. The current analytical results are found to be in good agreement with those of other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of micro gas film rotor-bearing systems.