<p>Could we prevent the death of a friend by travelling in time? Claims like this are usually settled by considering the structure of time: we could prevent their death provided time branches; we could not prevent their death if time is linear. Branching time allows changing timelines, and on some branches we might prevent their death. However, what would we say about the structure of time if, despite efforts under time-travel and repeated changes to the past, we continually failed to save our friend? In many time-travel fictions, certain events robustly reoccur across different branches. Some propositions, deaths especially, have an attraction despite changes to the past. In this essay I apply the notion of attractor from dynamical system theory to the set of possible worlds used to interpret a proposition within a Kripke model. A proposition is an attractor if there is a region of the model where the accessible worlds lead invariably to the extension of the proposition. Accessibility relations can have inevitable asymptotic structure. I argue that treating a proposition as an attractor in a Kripke model is a good way to provide an account of the inevitability of events.</p>