Fractals

Part 1 Models of irregular curves, S.Dubuc: examples of irregular curves; curves modelled by a functional equation; notions of dimension; calculating the size of a curve; applications. Part 2 Dyadic interpolation, G.Deslauriers and S.Dubuc. Part 3 Stochastic processes and covering procedures, M.Weber: some covering procedures; applications to the study of the regularity of stochastic processes - ultrametric structres. Part 4 Attractors and dimensions, P.Girault: some definitions; some theorems on the dimension of attractors; the Lorenz equations; some point transformations; the Navier-Stokes equations. Part 5 Construction of fractals and dimension problems, F.M.Dekking: a mathematical description of fractals; self-similarity properties; problems associated with determining the Hausdorff dimension. Part 6 Introduction to packing measures and dimensions, J.Peyriere. Part 7 Some remarks on Hausdorff dimension, J.L.Jonot. Part 8 Fractals, materials and energy, A.le Mehaute: fractals - where are they to be found?; on scales of measurement; the TEISI model; fractality and dissipation; why should the world be fractal?. Part 9 Problems concerning the concept of fractal in electrochemistry, M.Keddam: theoretical considerations; experimental considerations. Part 10 Some remarks concerning the structure of galactic clusters and Hubble's constant, P.Mills. Part 11 Disorder, chance and fractals in biology, G.Cherbit: glomerular filtration; pertubation of the rate of growth of a culture; bacterial division. Part 12 Fractals, semi-fractals and biometry, J.P.Rigaut: history; experimental methods; a semi-factal model; the lung as semi-fractal object; curvatures - relevant or not?; a gallery of semi-factal monsters; the frustration of the little quadrat. Part 13 Reconstruction of images from projections, N.de Beaucoudray, et al: data-collection methods using separate sections; tomographic reconstruction of images using the 3-dimensional Radon transform; codings with non-separated sections and not reducible to the 3-dimensional Radon transform. Part 14 Creation of fractal objects by diffusion, M.Rosso, et al. Part 15 Irreversibility and the time-arrow, J.Chanu. Part 16 Thermodynamic entropy and information, M.Courbage; information and thermodynamics; distance - information from one probability distribution wiht respect to another. Part 17 Dimension and entropy of regular curves, M.Mendes-France. Part 18 Local dimension, momentum and trajectories, G.Cherbit: local dimension - generalized velocity. Part 19 Space-time dimensionality, G.Cherbit.