Résumé : We describe in this paper an algorithm which dynamically maintains the trapezoidal map of an arrangement of line segments. This algorithm is a generalization of the Influence Graph data structure used by Boissonnat et al. to deal with the semi-dynamic case. Our complexity results are randomized, i.e. the insertion sequences are supposed to be evenly distributed among the n! possible sequences of $ segments, and when an object is deleted, we suppose that it can be any of the already inserted objects with the same probability. Under these assumptions the algorithm needs O(n+a) expected space, O(log n + a/n) expected insertion time, O( (1+ a/n)loglog n) expected deletion time and O(log n) time to locate any query point in the arrangement, where a is the current size of the arrangement and n the current number of segments.