Our experience of the world is a continuous stream of events, things occurring at a particular time and place. How this flow of experience is parsed and organized impacts our perception and memory of such events, yet the neural mechanisms underlying this process are largely unknown. The lateral entorhinal cortex may play a key role due its convergence of multisensory inputs, its encoding of events and their temporal relationships, and its connections with the hippocampal memory system. Here, we simultaneously recorded hundreds to thousands of neurons from lateral entorhinal cortex (LEC), medial entorhinal cortex (MEC), and area CA1 of the hippocampus in freely behaving adult male rats as we manipulated event structure. In the absence of defined events, population activity in LEC, but not MEC or CA1, continuously drifted along a one-dimensional manifold without reversing direction. After learning tasks with recurring events, LEC dynamics were constrained to stable state space trajectories defined by those events, while the drift was maintained along an orthogonal axis. Event boundaries in all tasks caused discrete shifts in state space, suggesting that LEC dynamics directly reflect event segmentation. Finally, continuous drift and discrete shifts are mechanistically distinct. Drift is driven by minute-scale variability in the firing rates of individual neurons while shifts are driven by synchronous activation of ensembles of neurons. Together, these results provide a dynamical systems explanation of how events are encoded within a temporal context.