Laurent Nottale

List of publications about:

"Scale Relativity, nondifferentiable geometry and fractal space-time".

Chronological order. April 2006.
(see page "downloable papers" for complete links)


  • Nottale, L., Schneider, J., 1984, J. Math. Phys., 25, 1296.
  • Nottale, L., 1988, C. R. Acad. Sc. Paris, 306, 341
  • Nottale, L., 1989, International Journal of Modern Physics, A4, 5047-5117
  • Nottale, L., 1990, in "Particle Astrophysics: The early Universe and Cosmic Structures", 10th Moriond Astrophysics meeting, eds. A. Blanchard and J. Tran Thanh Van (Frontières), p. 13.
  • Nottale, L., 1990, in "Applying Fractals in Astronomy", 2th Journées de Strasbourg, Eds. A. Heck and J. Perdang (Springer-Verlag), p. 181.
  • Nottale, L., 1991, in "Progress in Electromagnetics Research Symposium", Proceedings (Cambridge, USA), p. 754.
  • Nottale, L., 1992, International Journal of Modern Physics A7, 4899-4936   --> Version PDF
  • Nottale, L., 1992, invited conference, DISTANCIA'92, International Meeting on Distance Analysis (Rennes, France), S. Joly & G. Le Calvé eds., Université de Rennes, p.317.

  • BOOK:

    Nottale, L., 1993, (World Scientific, 1993), 333 pp.

    "Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity."

    For an on-line version (© World Scientific) of Chapter 1 (Introduction) and Chapter 2 (Relativity and Quantum Physics), click here.
    For the list of references of the book (alphabetical order): references.


  • Nottale, L., 1993, in "Cellular Automata: Prospects in Astrophysical Applications" , Université de Liège, A. Lejeune and J. Perdang (eds.), (World Scientific, 1993), pp.268-277.
  • Nottale, L., 1994, Chaos, Solitons & Fractals, 4, 361-388. Reprinted in "Quantum Mechanics, Diffusion and Chaotic Fractals", Eds. M.S. El Naschie, O.E. Rössler and I. Prigogine (Pergamon, 1995), p.51  ---> Version PDF
  • Nottale, L., 1994, invited conf., "First International Conference on Complex Systems in Computational Physics", Buenos-Aires, Ed. Marshall (Pergamon), Chaos, Solitons & Fractals 6, 401.   --->  Version PDF
  • Nottale, L., 1994, invited conference in "Relativity in General", E.R.E. 93 (Spanish Relativity Meeting) Salas, Ed. J. Diaz Alonso and M. Lorente Paramo (Frontières), p.121.   --->  Version PDF
  • Nottale, L., 1994, in "Le Big-Bang en question", Science et Vie Hors Série, 189, 116
  • Nottale, L., 1995, invited conference in "Chaos and diffusion in Hamiltonian systems", (Chamonix, Février 1994), Ed. D. Benest et C. Froeschlé (Frontière), pp 173-198.  --->  Version PDF
  • Nottale, L., 1995, in "Fractal Reviews in the Natural and Applied Sciences", Proceedings of "Fractals'95", Ed. M.M. Novak, (Chapman & Hall, London, 1995), pp. 12-23.
  • Nottale, L., 1995, Pour la Science, 215, 34 (Septembre 1995)
  • Nottale, L., 1995, in "Clustering in the Universe", 15th Moriond Astrophysics meeting, eds. S. Maurogordato, C. Balkowski, C. Tao and J. Tran Thanh Van (Frontières), p. 523  ---> Version PDF

  • Review paper:

    Nottale, L., 1996, Chaos, Solitons and Fractals, 7, 877-938

    "Scale Relativity and Fractal Space-Time: Application to Quantum Physics, Cosmology and Chaotic systems".  --> PostScript version     ---> PDF version


  • Nottale, L., 1996, Astron. Astrophys. Lett., 315, L9
  • Nottale, L., and Schumacher, G., Gay, J., 1997, Astron. Astrophys., 322, 1018-1025
  • Nottale, L., 1997, Astron. Astrophys., 327, 867
  • Nottale, L., 1997, in "Scale invariance and beyond", proceedings of Les Houches school, Ed. B. Dubrulle, F. Graner and D. Sornette, (EDP Sciences /Springer), p. 249.
  • Nottale, L., 1997, in Proceedings of I.A.C. colloquium, Paris 8 University, Intelligence artificielle et complexité, Ed. A. Ali Cherif et J. Signorini, p. 66
  • Nottale, L., 1997, in "Planetary systems: the long view", Proceedings of IXè rencontres de Blois, , Eds. L. Celnikier et J. Tran Thanh Van, Frontières, p. 51
  • Nottale, L., 1997, in Les Trous Noirs, Pour la Science (Dossier hors série), p.57.
  • Nottale, L., 1997, in Proceedings of Institute Kurt Bösch workshop, "Emergence, Entropy and the Creative Universe", Ed. T. Bernold, p. 155.
  • Nottale, L., 1997, in Proceedings of Colloquium "Dimension", Maison des Sciences de l'Homme, Eds. D. Flament, Chap. VIII.
  • Nottale, L., 1998, Ciel et Terre, Bulletin de la Société royale belge d'Astronomie, vol 114 (2), 63-71.
  • Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1035
  • Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1043
  • Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1051
  • Nottale, L. & Schumacher G., 1998, in "Fractals and beyond : Complexities in the Sciences", Proceedings of 'Fractal 98' conference, (World Scientific), Ed. M.M. Novak, p. 149.
  • "Scale relativity, fractal space-time and gravitational structures". --> pdf version

  • BOOK (in french):

  • Nottale, L., 1999, Chaos, Solitons and Fractals, 10, 459 (special issue)
  • Nottale, L., 1999, Proceedings of I.A.C.'98 colloquium, Paris 8 University, Intelligence artificielle et complexité, Eds. A. Ali Cherif et J. Signorini, p. 51
  • Chaline, J., Nottale, L., Grou, P., 1999, C.R. Acad. Sci. Paris, 328, 717
  • Chaline J., Nottale L. et Grou P., 1999, C. R. Acad. Sci. Paris, 328, IIa, 717-726.
  • Nottale, L., 1999, La Mazarine, Oct. 1999, 10, p. 21.
  • Nottale, L., Schumacher, G., & Lefèvre, E.T., 2000, Astron. Astrophys. 361, 379
  • Nottale, L., Galopeau, P.H.M., & Lefèvre, E.T., 2000, Physics and Chemistry of the Earth, preprint
  • Nottale, L., 2000, Proceedings of 4è Forum Halieumétrique (Juin 1999), Les espaces de l'halieutique, Eds. D. Gascuel, P. Chavance, N. Bez & A. Biseau, IRD Editions, p.41
  • Nottale, L., 1999, in Temps, an 2000, ed. Desjeunes
  • Nottale, L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars 2001, p. 11-25
  • Nottale, L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars 2001, p. 93-116
  • Nottale, L., 2000, in Séminaire "Histoires de géométries", Maison des sciences de l'homme, Ed. D. Flament, p.1
  • Nottale, L., 2000, in Science of the Interface, Proceedings of International Colloquium in honor of Otto Rössler, ZKM Karlsruhe, 18-21 May 2000, Eds. H. Diebner, T. Druckney and P. Weibel, p. 38 (Genista Verlag, Tübingen, 2001)
  • Nottale, L., Chaline, J., & Grou, P. 2000, in "Fractals in Biology and Medicine", Proceedings of Fractal 2000 Third International Symposium, Ed. G. Losa, Birckhäuser Verlag, p. 247


  • Nottale, L., 2001, in Frontiers of Fundamental Physics, Proceedings of Birla Science Center Fourth International Symposium, 11-13 dec. 2000, Hyderabad, India, Eds. B.G. Sidharth and M.V. Altaisky, (Kluwer Academic), p. 65.   --> version ps   --> version pdf
  • "Scale relativity and non-differentiable fractal space-time".
  • Nottale, L., 2002, in Traité IC2, "Lois d'échelle, fractales et ondelettes", eds. P. Abry, P. Gonçalvès et J. Levy Vehel, (Hermès 2002), Vol. 2, Chap. 7, p. 233
  • Nottale, L., 1998-2002, Web pages, http://www.daec.obspm.fr/users/nottale/index.html
  • "Scale relativity and fractal space-time".
  • Nottale, L. & Tran Minh N., 2001, Actualités / Nouvelles Scientifiques, Observatoire de Paris, Mai 2001, http://www.obspm.fr/actual/nouvelle/nottale/nouv.fr.shtml
  • Cash R., Chaline, J., Nottale, L., Grou, P., 2002, C.R. Biologies  325, 585-590
  • Nottale L., 2002, invited conference in International Colloquium "Géométrie au XXè siècle", Paris, 24-29 Septembre 2001   --> Version ps   --> version pdf
  • Nottale, L., 2002, in Vè Symposium "Mathématiques et Dialyse" (Pyramide du Louvre, Paris, 13 Novembre 2000), N.K. Man, B. Perrone, T. Petitclerc coordonnateurs (Meditor, Strasbourg), p. 3.
  • Nottale, L., 2002, in La complexité, vertiges et promesses, 18 histoires de sciences (entretiens avec Morin, Prigogine, Gershensfeld, Mange, Deneubourg, Steels, Langton, Varela, Goodwin, Kauffman, Derrida, Pomeau, Ekeland, Chaitin, Barrow, Nottale, Linde, Serres), ed. Reda Benkirane, Le Pommier, Chap. XVI, pp. 329-356
  • Nottale, L., 2002, in "Penser les limites. Ecrits en l'honneur d'André Green", Delachiaux et Niestlé, p. 157.
  • P. Galopeau, L. Nottale, D. Da Rocha, N. Tran Minh, C. Mégessier et G. Schumacher, 2002, Actes du 3e Colloque du Programme National de Planétologie de líINSU, eds. O. Grasset, A. Cossard et C. Sotin, pp. 18-19.
  • Nottale, L., 2003, Chaos, Solitons and Fractals, 16, 539   --> Version ps  --> Version pdf
  • Da Rocha D. & Nottale, L., 2003, Chaos, Solitons and Fractals, 16, 565   -->  Version pdf
  • Nottale, L., 2003, Electromagnetic Phenomena, T. 3, N°1 (9), 24 --> Version ps  --> pdf version
  • Célérier, M.N., Nottale, L., 2003, Electromagnetic Phenomena, T. 3, N°1 (9), 83 (eprint hep-th/0210027)
  • Nottale, L., 2003, L'Astronomie 117,3
  • Nottale, L., 2003, Pour La Science, 309, 38-45 (Juillet 2003)
  • Da Rocha D. & Nottale, L., 2003, in  Colloquium "Winds, Bubbles, and Explosions: a conference to honor John Dyson", Pátzcuaro, Michoacán, México, September 9-13, 2002 (Eds. S. J. Arthur & W. J. Henney) Revista Mexicana de Astronomía y Astrofísica (Serie de Conferencias) Vol. 15, p. 69
  • Nottale, L., 2003, Siècle 21 Littérature & société, 2è année n°2, pp. 149-154
  • Nottale L., 2003, Science & Conscience 11, 62-67.
  • Grou P., Nottale L., Chaline J., 2004, in "Zona Arqueologica, Miscelanea en homenaje a Emiliano Aguirre", IV Arqueologia : 230-237, Museo Arquelogico Regional, Madrid.
  • Célérier M.-N. & Nottale, L., 2004, J. Phys. A, 37, 931-955
  • Nottale L., 2004, invited conference, in "Computing Anticipatory Systems. CASYS'03 - Sixth International Conference" (Liège, Belgique, 11-16 Août 2003), Daniel M. Dubois Editor, American Institute of Physics Conference Proceedings  718, 68-95
  • Nottale L, Galopeau P., Ceccolini D. Da Rocha D. Schumacher G. & Tran-Minh N., 2004, in "Extrasolar Planets: Today and Tomorrow", XIXè colloque IAP (Paris, France), 30 June-4 July 2003, Eds. J.P. Beaulieu, A. Lecavelier and C. Terquem, ASP Conference Proceeding 321, 355
  • Nottale L., 2005, invited contribution in the volume "Trends in Field Theory Research", (Nova Science), in press
  • Nottale L., 2004, in G. Ord, P. Weibel, O. Rössler (Eds.) , Springer Vienna, in press
  • Nottale L., 2004, Proceedings of Symposia in Pure mathematics, , 72, Part 1, p. 57 (American Mathematical Society, Providence)
  • Nottale L., 2004, in "Scientific Highlights 2004", Proceedings of the Journées de la SF2A, Paris 14-18 Juin 2004, F. Combes & D. Barret eds., EDP Sciences, p. 373
  • Célérier M.N. & Nottale L., 2004, in "Scientific Highlights 2004", Proceedings of the Journées de la SF2A, Paris 14-18 Juin 2004, F. Combes & D. Barret eds., EDP Sciences, p. 649
  • Lehner T., Nottale L., di Menza L., da Rocha D., & Ceccolini D., 2004, in "Scientific Highlights 2004", Proceedings of the Journées de la SF2A, Paris 14-18 Juin 2004, F. Combes & D. Barret eds., EDP Sciences, p. 687
  • Nottale L., 2004,  in "Scientific Highlights 2004", Proceedings of the Journées de la SF2A, Paris 14-18 Juin 2004, F. Combes & D. Barret eds., EDP Sciences, p. 699
  • Galopeau P., Nottale L., Ceccolini D., da Rocha D., Schumacher G. & Tran-Minh N., 2004, in "Scientific Highlights 2004", Proceedings of the Journées de la SF2A, Paris 14-18 Juin 2004, F. Combes & D. Barret eds., EDP Sciences, p. 75
  • Nottale L., 2005, Progress in Physics, 1, 12-16
  • Auffray C., Nottale L. & the Systemoscope Consortium, Invited Conference in International Conference "Integrative Systems Biology for Health - TRANSCRIPTOME 2005", Shanghai, Chine, 5-9 Novembre 2005
  • Nottale L., Célérier M.N., Lehner T., 2006, J. Math. Phys. 47, 032303 (eprint hep-th/0307093)
  • Nottale L. 2006, in Proceedings of 7th International Colloquium on Clifford Algebra, Ed. P. Anglès (Birkhauser, 2006)
  • Nottale L. 2006, Invited Conference in "Frontiers of Fundamental Physics", Proceedings of the Sixth International Symposium "Frontiers of Fundamental and Computational Physics", Udine, Italy, 26-29 September 2004, Sidharth, B.G., Honsell, F. & de Angelis, A. (Eds.)
  • Nottale L. 2006, Invited Conference, Proceedings du Congrès FFN, Paris 2005, sous presse

  • Others publications about scale relativity (not exhaustive)
     

  •  Ben Adda F. and Cresson J., 2000, C. R. Acad. Sci. Paris, 330, Série I, p. 261
  • Ben Adda F. and Cresson J.,  2001, Journ. Mathematical Analysis and Applications 263, 721
  • Castro, C., Foundations of Physics Lett., 10, 273
  •  Castro, C., preprint hep-th/9612003
  •  Cresson J., 2002, Chaos Solitons and Fractals 14, 553
  • Dubrulle, B. & Graner F., 1996, J. Phys. II (Fr) 6, 797.
  • Altaisky, M.V., 1996, Differential Equations and Dynamical Systems, Vol. 4, N. 3/4, 267
  • "On some geometrical consequences of the incorporation of resolution in the definition of a coordinate system"
  • Hermann, R. P., 1997, J. Phys. A30, 3967-3975, 1997
  • Herrmann, F., 1997, Ph.D. Thesis, Delft University of Technology, The Netherlands
  • Hermann R., Schumacher G., Guyard R., 1998, Astron. Astrophys. 335, 284   (PDF)
  • "Scale relativity and quantization of the solar system. Orbit quantization of the planetís satellites"
  • Laperashvili L.V., Ryzhikh D.A., 2001,  arXiv:hep-th/0110127
  • "Phase transition in Gauge Theories and the Planck Scale Physics"
  • Pissondes, J.C., 1999, Chaos, Solitons and Fractals 10, 513
  • Pissondes, J.C., 1999, J. Phys. A: Math. Gen. 32, 2871  (PDF)
  • Jumarie, G., 2001, Int. J. Mod. Phys. A 16, 5061
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