A hybrid automaton is a digital, real-time system that interacts with an analogue environment. In this talk, we introduce a denotational semantics for non-linear hybrid automata and relate it to the operational semantics given in terms of hybrid trajectories. The semantics is defined as least fixpoint of an operator on the continuous domain of functions of time that take values in the lattice of compact subsets of n-dimensional Euclidean space. The semantic function assigns to every point in time the set of states the automaton can visit at that time, starting from one of its initial states. The main results are the correctness and computational adequacy of the denotational semantics with respect to the operational semantics given in terms of hybrid trajectories. Moreover, we show that the denotational semantics can be effectively computed, which allows for the effective analysis of a large class of non-linear hybrid automata.