Space-time contraction and the dynamics of urban systems

An attempt is made to identify the dynamics of urban systems during the historical process of their evolution. An illustration is made with the case of European cities between 1200 and 1990, using harmonised historical data bases. Simple maps show first a general expansion in cities number and size over time, reflecting the ability of the system to continuously adapt its structure over time. A second trend is an increased hierarchisation in city size, which may be related to the continuous improvement in the speed and capacity of transportation means. Because of this space-time contraction, large cities short-circuit small towns, and inequalities in city size are widening. A third trend leading to a spatial reorganisation, emerges from maps of the urban population potentials. Among all possible mathematical equations and parameters values which could describe the intensity and the spatial range of interactions between cities, we choose those which give rather stable results and which are compatible with the analysis of urban historians, as De Vries, Braudel, Bairoch, Hohenberg and Lees, for the centuries preceding industrial revolution, by using evaluations of distances in terms of time and cost. Urban systems dynamics is better approached with reference to this relative space than on usual topographic maps