Géométrie fractale et phénomènes chaotiques
Ce cours est enseigné à Supelec depuis 2007. Il est composé de 5 séances (chaque de 3 heures) et l'examen oral.
Séance 1 : Géométrie fractale
B. Mandelbrot, The Fractal Geometry of Nature (San Francisco, Freeman, 1982).
J.-F. Gouyet, Physics and Fractal Structures (Springer Verlag Gmbh, 1996)
J. Feder, Fractals (New York, Plenum Press, 1988).
K. J. Falconer, The Geometry of Fractal Sets (Cambridge, England Cambridge University Press, 1986).
B. Sapoval, Universalité et fractales (Paris, Flammarion, coll. Champs., 2001).
P. Bak, How Nature Works: The Science of Self-Organized Criticality (New York: Copernicus, 1996).
Séance 2 : Mouvement brownien
J. Klafter and I. M. Sokolov, First Steps in Random Walks: From Tools to Applications
(Oxford University Press, 2011)
W. Feller, An Introduction to Probability Theory and Its Applications, Volumes I and II, Second Edition (John Wiley & Sons, New York, 1971).
P. Levy, Processus stochastiques et movement brownien (Paris, Gauthier-Villard, 1965).
S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001).
Séance 3 : Dynamique chaotique
E. Lorenz, The Essence of Chaos (University of Washington Press, 1996).
M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, 1990).
S. H. Kellert, In the Wake of Chaos: Unpredictable Order in Dynamical Systems (University of Chicago Press, 1993).
P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems (Birkhauser, 1980).
R. Kautz, Chaos: The Science of Predictable Random Motion (Oxford University Press, 2011)
F. Moon, Chaotic and Fractal Dynamics (Springer-Verlag, 1990).
P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, 2004).
J. Mathieu and J. Scott, An Introduction to Turbulent Flow (Cambridge University Press, 2000).
J. Cardy, G. Falkovich and K. Gawedzki, Non-equilibrium statistical mechanics and turbulence (Cambridge University Press, 2008).
T. Bohr, M. H. Jensen, G. Paladin and A. Vulpiani, Dynamical Systems Approach to Turbulence (Cambridge University Press, 1998)
P. A. Durbin and B. A. Pettersson Reif, Statistical Theory and Modeling for Turbulent Flows (Johns Wiley & Sons, 2001).
Séance 4 : Phénomènes de croissance
T. Vicsek, Fractal Growth Phenomena, 2nd ed. (Singapore, World Scientific, 1992).
R. B. Banks, Growth and Diffusion Phenomena: Mathematical Frameworks and Applications (Springer Science & Business Media, 1994)
P. L. Krapivsky, S. Redner, E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge, Cambridge University Press, 2010).
Séance 5a: Percolation
D. Stauffer and A. Aharony, Introduction to Percolation Theory (2nd Ed., Taylor and Francis, London, 1994)
M. Sahimi, Applications of Percolation Theory (Taylor & Francis, London, 1994)
D. Ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, 2000)
Séance 5b: Ondelettes
I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, 1992)
S. Mallat, A wavelet tour of signal processing (2nd Ed., Academic Press, 1999)
Y. Meyer, Wavelets and Operators (Cambridge Studies in Advanced Mathematics, Vol. 37, 1993)
Other references
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Dernière mise à jour le 18/10/2014