We aim to better understand the dynamics within relativistic magneto-hydrodynamical flows in the extreme environment and close vicinity of supermassive black holes. To do so, we analyze the peculiar radio galaxy 3C 111, for which long-term polarimetric observations are available. We make use of the high spatial resolution of the VLBA network and the MOJAVE monitoring program, which provides high data quality also for single sources and allows us to study jet dynamics on parsec scales in full polarization with an evenly sampled time-domain. We additionally consider data from the IRAM 30-m Telescope as well as the SMA. Jet properties such as the electric vectors, the (polarized) flux density, feature size, and brightness temperature, describe a complex evolution of the polarized jet. The electric vector position angles (EVPAs) of features traveling down the jet perform a large and smooth rotation of $gtrsim 180^{circ}$ across a distance of about 20 pc. In contrast, the EVPAs are strongly variable within the first parsecs of the jet. We find a tendency towards transverse EVPAs across the jet with a local anomaly of aligned vectors in between. The transverse extent of the flow decreases coincident with a jump in brightness temperature around where we observe the EVPAs to turn into alignment with the jet flow. Also the gradients of the feature size and particle density with distance steepen in that region. We interpret the propagating polarized features with shocks and the observed local anomalies with the interaction of these shocks with a recollimation shock of the underlying flow. Together with a sheared magnetic field, this shock-shock interaction can explain the large rotation of the EVPA. The superimposed variability of the EVPAs close to the core is likely related to a clumpy Faraday screen, which also contributes significantly to the observed EVPA rotation in that region.
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