Wavelet analysis and applications to some dynamical systems

Argoul F., Arneodo A., Grasseau G., Gagne Y., Hopfinger E.J. Frisch U.: 1989, “Wavelet analysis of turbulence reveals the multifractal nature of the Richardson cascade”,Nature 338, 51–53 Arneodo A., Grasseau G., Holschneider M.: 1988, “Wavelet transform of multifractals”,Phys. Rev. Lett. 61, 2281–2284 Arneodo A., Grasseau G., Holschneider M.: 1989, “Wavelet transform analysis of invariant measures of some dynamical systems”,Wavelets, Time-Frequency Methods in Phase Space, (Combes J.M., Grossmann A. and Tchamitchian Ph. Eds.) Springer-Verlag, 182–196 Arnéodo A., Argoul F., Grasseau G.: 1990, “Transformation en ondelettes et renormalisation”,Les ondelettes en 1989, (Lemarié P.G. Ed.), 125–187 Arnold: 1969,Astron J.,74, 1235–1242 Barlaud M., Mathieu P., Antonini M.: 1989),Proc. of the 6 th IEEE Multidimensional Signal processing Workshop, New York, 103 Bendjoya Ph., Slézak E., Froeschlé Cl.: 1991, “The wavelet transform: a new tool for asteroid family determination”,Astron. Astroph. 251, 312–330 Bendjoya Ph., Cellino A.: 1991b, “Asteroid families identified by two different methods”,Compte rendus de l'école de Goutelas Froeschlé Cl., Benest D. (Eds) Edition Frontiere, (in press) Bendjoya Ph., Cellino A., Zappala V., Froeschlé Cl.: 1991c, “Simulated families: a test for different methods of family identification”,Asteroid Comets Meteors 91, (Harris A., Bowell T. Eds), in press Bendjoya Ph., Cellino A., Froeschlé Cl., Zappala V.: (1992)in preparation Bergé P., Pommeau Y., Vidal Ch.: 1984, “L'ordre dans le chaos”,Hermann Ed., Paris Bergé P., Dubois M.: 1988, “Etude experimentale de transition vers le chaos en convection de Rayleigh-Benard”,Le Chaos (Eyrolles Ed.), 1–83 Bessis D., Fournier J.D., Servizi G., Tuschetti G., Vaienti S.: 1987,Phys. Rev. A 36, 920 Bijaoui A., Giudicelli M.: 1991,Experimental Astronomy,1, 347–363 Bijaoui A.: 1991, “Algorithme de la transformée ondelette: application à l'imagerie astronomique”,Ondelettes et paquets d'ondes. Cours CEA, EDF, INRIA, 125–140 Brouwer D.: 1951,Astron J.,56, 9 Coullet P., Tresser C.: 1978),J. Physique, Colloq,39, C5 Carusi and Valsecchi G.: 1982,Astron. Astroph.,115, 327 Coullet P., Treeser C., Tirapegui: 1981,Field Theory, Quantization and Statistical Physic, (Reidel D. Publishing Company, Dordrecht), 249 Collet P., Lebowitz J., Porzio A.: 1987,J. Stat. Phys.,47, 609 Daubechies I.: 1989, “Wavelets: a tool for time-frequency analysis”,Proc. of the 6 th IEEE Multidimensional Signal processing Worshop, New York, 98 Dutilleux P..: 1989, “An implementation of the ‘algorithme a trou’ to compute the wavelet trans-form”,Wavelets, Time-Frequency Methods in Phase Space, (Combes J.M., Grossmann A. and Tchamitchian Ph. Eds.), Springer-Verlag, 298–304 Feigenbaum M.J.: 1978),J. Stat. Phys.,19, 25 Flandrin P.: 1987, “Some aspect of non-stationary signal processing with emphasis on time frequency and time-scale methods”,Wavelets Time-Frequency Methods in Phase Space (Combes J.M., Grossmann A. and Tchamitchian Ph. Eds.), Springer-Verlag, 68–99 Fournier J. D., Frisch U.: 1983, “L'équation de Burgers déterministe et statistique”,Journal de Mécanique Théorique et Appliquée,2, 699–750 Frisch U., Sulem P.L., Nelkin M.: 1978,J. Fluid. Mech.,87, 719 Frisch U.: 1985, “Turbulence and predictability in geophysical fluid dynamics and climate dynamics”,Compte-Rendus Ecole Intern. “Enrico Fermi”, Ghil M., Benzi R., Parisi G. Eds (North Holland, Amsterdam) Frisch U.: 1985,Physica Scripta,T9, 137 gilbert A.D., Froeschlé Cl. and Frisch U.: 1993,in this volume Gabor D.: 1946,J. IEEE,93, (III) 429–457 Gagne Y.: 1987,Thesis, Univ. de Grenoble Grossmann A., Kronland-Martinet R., and Morlet J.: 1987, “Reading and understanding continuous wavelet transform”,Wavelets, Time-Frequency Methods in Phase Space, (Combes J.M., Grossmann A. and Tchamitchian Ph. Eds.), Springer-Verlag, 2–20 Guillemain P., Kronland-Martinet R., Martens B.: 1989, “Application de la transformée en ondelette en spectroscopie RNM”,Note-LMA, 112. Halsey T.C., Jensen M.H, Kadanoff L.P., Procaccia I., Shraiman B.I.: 1986),Phys. Rev. A,33, 1141 Hirayama K.: 1918, “Group of asteroids probably of common origin”,Proc. Phys.-Math. Soc. Japan,11, 354–361 Holschneider M.: 1988,J. Stat. Phys.,50, 963 Kozai Y.: 1979,Asteroid, (Gehrels T. Ed. University of Arizona, Tucson), 334–358 Kronland-Martinet R., Morlet J., Grossmann A.: 1987, “Analysis of sound patterns through wavelet transform”,International Journal of Pattern Recognition and Artificial Intelligence, 273–302 Liandrat J., Perrier V. Tchamitchian Ph.: 1990, “Numerical resolution of the 1D regularized Burgers equation using a spatial wavelet approximation algorithm and numerical results”,ICASE Report, NASA, Hampton, Virginia Linblad B.A., Southworth: 1971),Physical Studies of Minor Planets, (Gehrels T. Ed. NASA SP-267, Washington DC: US Government Printing Office), 337–352 Loisel P.: 1986, “Resolution des equations de Navier-Stokes compressibles instationaires par methodes spectrales de Tchebycheff”,Thesis, Paris VI Jones B.J.T., Martinez V.J., Saar E., Einasto J.: 1988, “Multifractal description of large scale structure of the universe”,Astroph. J.,352, L1-L5 Mallat S. G.: 1989, “A theory for multiresolution signal decomposition: the wavelet representation”,IEEE Trans. on Pattern Anal. and Machine Intell.,11, 674–693 Morlet J., Arens G., Fourgeau I., Giard D.: 1982, “Wave propagation and sampling theory”,Geophysics,47, 203–236 Milani A., Knezevic Z.: 1990,Celestial Mechanics,4, 347–412 Milani A., Farinella P., Knezevic Z.: 1991, “On the search for asteroid families”,Compte rendus de l 'école de Goutelas, Froeschlé Cl., Benest D. (Eds) Edition Frontiere, (in press) Murenzi R: 1990, “Ondelettes multidimensionnelles et applications à l'analyse d'images”,Thesis, Université catholique de Louvain Muzy J.F., Barcy E., Arneodo A.: 1991, “Wavelets and multifractal formalism for singular signals: application to turbulence data”,Phys. Rev. Let.,67, 3515–3518 Pernaud-Thomas B.: 1988, “Méthodes numériques d'ordre élevé appliquées aux calculs d' écoulements compressibles”,Thesis, Paris VI Perrier V.: 1989, “Towards a method for solving partial differential equations using wavelet basis”,Wavelets, Time-Frequency Methods in Phase Space, (Combes J.M., Grossmann A. and Tchamitchian Ph. Eds.), Springer-Verlag, 269–283 Ruelle D., Takens F.: 1971, “On the nature of turbulence”,Mathematical Physics,20, 167 Richardson L.F.: 1922,Weather Prediction by Numerical Process, Cambridge Univ. Press Starck J.L., Bijaoui A.: 1991, “Filtering and restoration with the wavelet transform”, 3rd ESO data analysis workshop Slézak E., Bijaoui A., Mars G.: 1990, “Identification of structures from galaxy count: use of the wavelet transform”,Astron. Astroph.,227, 301–316 Tresser C., Coullet P.: 1978,C. R. Acad. Sci.,287, 577 Vergassola M., Frisch U.: 1991, “Wavelet transforms of self-similar processes”,Physica D,54, 58–64 Wickerhauser M. V.: 1991, “INRIA Lectures on wavelet packets algorithm”, YALE University preprint Williams J.G.: 1971,Physical studies of minor planets (Gehrels T. Ed. NASA SP-267, Washington DC: US Government printing office), 177–181 Zappala V., Farinella P., Knezevic Z., Paolicchi P.: 1984, “Collisional origin of the asteroid families: Mass and velocity distributions”,Icarus,59 261–285 Zappala V., Cellino A., Farinella P., Knezevic Z.: 1990, “Asteroid families: identification by hierarchical clustering and reliability assessment”,Astron J.,100, 2030–2046