A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.
From his early economic works on, Marx conceived the labour of any kind of society as a set of production activities and analysed the historical modes of production as specific ways of distributing and exchanging these activities. Political economy on the contrary considers the labour only under the form of its product, and the exchange of products as commodities as the unique form of social labour exchange. For Marx, insofar as the labour creating value represents a specific mode of exchanging the society's living labour, general and abstract labour cannot not only be defined as the substance or measure unit of the commodity, as in Smith or Ricardo, but foremost as an expense of living labour, i.e. of nerves, muscles, brain, etc. Hence the twofold nature of living labour, as a concrete activity producing a use value and an expense of human labour in general producing exchange value. Marx himself claimed that this twofold nature of labour creating value was its main and most important contribution to economic science. This book aims at showing how both determines the original categories and economic laws in Capital and constitutes the profound innerspring of Marx's critique of political economy. The role and function of living labour is highlighted by dealing with the difference between Marx and Classics' theories of labour value; money and the problems of its integration in economic analysis, especially in Keynes; the transition from feudalism to capitalism; the theory of capital through a discussion on the Cambridge controversy and the transformation problem; the labour process and the principles of labour management; unemployment and overpopulation; the formulas of capital in the history of economic thought; finally, an interpretation of the current crisis based on Marx's conception of overaccumulation and speculation after having distinguished it from underconsumption and stagnation theories of crises.
A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.
Retrospective exhibition of twenty-five years of ... [Yves Saint Laurent's] work ... This book, published in connection with the exhibition, features over two hundred of Saint Laurent's couture designs, more than seventy in full color ... Also included is a fully illustrated survey of Saint Laurent's work photographed in black and white by Pierre Boulat and Nicholas Vreeland, supplemented by historically important photographs published in the fashion magazines of the era taken by such renowned photographers as Richard Avedon, Irving Penn, Bert Stern, Neal Barr, and Bill King"--Cover.
This illustrated volume presents vibrant photographs of Yves Saint Laurent's most important designs and is highlighted with essays and quotations that honor his legacy.
Paris, le 6 décembre 1986. Suite une manifestation estudiantine contre le projet de réforme universitaire du ministre délégué Alain Devaquet une tragique bavure policière entraîne la mort de Malik Oussekine, jeune étudiant de 22 ans. A la suite de cette tragédie, Devaquet présente sa démission. 30 ans après Jeanne Puchol et Laurent-Frédéric Bollée ravivent notre attention sur cet événement très médiatisé, qui aujourd'hui encore trouve des retentissements dans une France en proie à de nombreux troubles sociaux.
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