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"Depuis une trentaine d'années, les approches fractales se sont multipliées dans des domaines nombreux et variés. Malgré les difficultés inhérentes à la collaboration des disciplines, mais grâce au développement remarquable des méthodes et moyens de calcul, on a observé des avancées significatives. Pour ce qui est de l'aménagement des territoires, des villes, des transports, des pionniers ont montré le chemin dès le début des années 1990. Aujourd'hui des voies sont tracées. Des applications existent pour cerner l'occupation fractale des espaces par les populations, les bâtiments et les formes fractales de leur desserte par les réseaux. Ce livre présente les résultats et les réflexions les plus actuels sur ces sujets. Il met en exergue l'apport des fractales pour comprendre, prévoir et agir face aux redoutables défis qui se présentent aujourd'hui, tant pour les professionnels que pour les politiques : durabilité, mobilité, intégration, justice spatiale."

Réseaux (aménagement du territoire) --- Mobilité spatiale --- Transports urbains --- Modèles mathématiques --- Cities and towns --- Fractals --- City planning --- Growth --- Mathematical models --- Modèles mathématiques. --- Cities and towns - Growth - Mathematical models --- City planning - Mathematical models

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Zipf's law is one of the few quantitative reproducible regularities found in economics. It states that, for most countries, the size distributions of city sizes and of firms are power laws with a specific exponent: the number of cities and of firms with sizes greater than S is inversely proportional to S. Zipf's law also holds in many other scientific fields. Most explanations start with Gibrat's law of proportional growth (also known as "preferential attachment'' in the application to network growth) but need to incorporate additional constraints and ingredients introducing deviations from it. This book presents a general theoretical derivation of Zipf's law, providing a synthesis and extension of previous approaches. The general theory is presented in the language of firm dynamics for the sake of convenience but applies to many other systems. It takes into account (i) time-varying firm creation, (ii) firm's exit resulting from both a lack of sufficient capital and sudden external shocks, (iii) the coupling between firm's birth rate and the growth of the value of the population of firms. The robustness of Zipf's law is understood from the approximate validity of a general balance condition. A classification of the mechanisms responsible for deviations from Zipf's law is also offered.

Cities and towns -- Growth -- Mathematical models. --- Economic geography -- Mathematical models. --- Urban economics -- Mathematical models. --- Zipf’s law. --- Urban economics --- Economic geography --- Zipf's law --- Cities and towns --- Sociology & Social History --- Finance --- Business & Economics --- Economic History --- Finance - General --- Communities - Urban Groups --- Social Sciences --- Mathematical models --- Growth --- Zipf's law. --- Mathematical models. --- Geographic models --- Probabilities. --- Economic theory. --- Macroeconomics. --- Economics. --- Macroeconomics/Monetary Economics//Financial Economics. --- Probability Theory and Stochastic Processes. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Language and languages --- Word frequency --- Distribution (Probability theory. --- Economics --- Economic theory --- Political economy --- Social sciences --- Economic man --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk