Parkinson's Disease is a progressive disorder of the nervous system that affects the motor system of the patients, producing several impairments in muscles and limbs. One of the major manifestations of the disease appears in gait, and typically causes disability of the patients. Gait assessment appears as an useful tool to support the diagnosis process and to evaluate the neurological state of the patients. The gait of the patients is mainly evaluated from signals captured with inertial sensors attached to the limbs of the patients, where kinematics features are commonly computed. On the other hand, there are non-linear effects of the gait process that cannot be properly characterized with the kinematic features. This study proposes the use several non-linear dynamics features to assess the gait impairments of Parkinson's patients. We consider classical non-linear features such as the correlation dimension, the largest Lyapunov exponent, and the Hurst exponent, among others. In addition we propose a novel non-linear analysis based on applying a Gaussian mixture model to find clusters in Poincaré sections. The non-linear dynamics features are used to discriminate between Parkinson's patients and healthy subjects, and