Abstract
Using numerical relativity simulations we study the dynamics of pseudo-topological objects called oscillons for a class of models inspired by axion-monodromy. Starting from free field solutions supported by gravitational attractions, we investigate the effect of adding self-interactions, and contrast this with the effect of adding self-interactions whilst removing gravitational support. We map out regions of the parameter space where the initial conditions rapidly collapse to black holes, and other regions where they remain pseudo-stable or disperse.