Algorithmic recourse aims to provide individuals affected by a negative classification outcome with actions which, if applied, would flip this outcome. Various approaches to the generation of recourse have been proposed in the literature; these are typically assessed on statistical measures such as the validity of generated explanations or their proximity to the training data. However, little to no attention has been paid to the underlying dynamics of recourse. If a group of individuals applies the suggested actions, they may over time induce a shift in the domain or model. We propose a framework for the measurement of such intrinsic shifts, and conduct an analysis of the dynamics of recourse implemented by the generators proposed by Mothilal et al. and Wachter et al.. Our results suggest that the application of recourse is likely to introduce statistically significant shifts in the system, and that the underlying dataset and model impact the behavior of the generators.